Perpendicular Definition and 503 Threads

Homework Statement Find a vector perpendicular to plane z = 5 + 3x - y, and find a vector parallel to the plane. Homework Equations The Attempt at a Solution The normal vector is simple, because my book addresses it. It is 3i - j - k. I have absolutely no clue how to get a...

If I have a vector nhat = [nx, ny, nz] which is normal to some plane, how can I write the vectors (I assume there are infinitely many) which are perpendicular to that plane?

Homework Statement (b) Show that the equation of the perpendicular bisector of the line segment with endpoints (x_{1}, y_{1}) and (x_{2},y_{2}) can be written as \frac{x-x^{-}}{y_{2}-y_{1}}+\frac{y-y^{-}}{x_{2}-x_{1}}= 0, where (x^{-},y^{-})are coordinates of the midpoint of the segment The...

If u stand on top of a spaceship, u will not be thrust backward? U only do on top of an airplane because of air resistance? So if u jump up out of a horizontally moving spaceship, after you jump out you are moving with the same horizontal speed as you were inside the spaceship? U just have to...

for the following two vectors find the constant 'p' such that the vectors a & b are perpendicular: a = i + 2pj +3pk b = i - 2j + pk the answer is: p = 1 & p = 1/3, but how is this calculated? any help would be massively appreciated i understand that the angle between the vectors...

Homework Statement Given two vectors A=9i+1j+9k and B=12i-12j+10k find: a) Their dot product AB b) Their cross product AxB c)The angle between the vectors A and B d) a vector C that is parallel with A and has the same magnitude as B e) A vector C that is perpendicular to A and has the...

I asked a similar question about gravity, but I would just like to check the math of this first. In the first picture I have a circle of radius r, There is a point p on the circle, and I am first trying to show that the equation below gives the area of the circle: 2\int^{90}_{0} \frac{\pi...

Two unequal masses m and 2m are attached to a thin bar of negligible mass that rotates about an axis perpendicular to the bar. When m is a distance 2d from the axis and 2m is a distance d from the axis, the moment of inertia of this combination is I. If the masses are now interchanged, the...

Hi, Why is the Acceleration vector (second derivative) perpendicular to the tangent (first derivative) when velocity is constant ? I understand that when velocity is constant there is no acceleration but it's that vector being perpendicular to its tangent is confusing me. For example...

does friction restrict motion perpendicular to the plane also?? Friction is caused due to cold weld between the molecules of the surface and the object.So why does it only affect the motion parallel to surface. Because even when we move a body straight up the cold weld needs to be broken.

Homework Statement Find the perpendicular distance from the point (1,2,3) to the plane x-2y-z=1 One method: find the equation of the line throughout (1,2,3) perpendicular to the plane. Find the intersection of this line and the plane The Attempt at a Solution I know the vector...

Homework Statement Let U be a subspace of ℝn. Show that if u\inU\bigcapU\bot, then u=0. Homework Equations The Attempt at a Solution I know that U\bot will be orthogonal to U, so any vector u in U dotted with any vector in U\bot will equal 0. But that does not necessarily mean...

Homework Statement Find an equation for the line perpendicular to the tangent to the curve y=x^3-4x+1 at the point (2,1).Homework Equations point slope form, m * (-1/m) = -1The Attempt at a Solution Derivate: y+3x^2-4 m=8 at x=2 Tangent line: y=8x-15 Answer: y=-x/8-15 Answer in book, y=-x/8 +...

Homework Statement Find the perpendicular distance of the plane 5x+2y-z=-22 from the origin O by first finding the co-ordinates of the point P on the plane such that OP is perpendicular to the given plane. Homework Equations It only given plane vector,how i going to figure out the...

Homework Statement Find the perpendicular distance between y=2x-1 and y=2x - 8/3 2. The attempt at a solution The first equation hits the y-axis at -1 and the other at -8/3, which means the vertical (y axis) distance between them is 5/3, but to use trig, I need another piece of...

Homework Statement Find equation of the line which is perpendicular to the line and has y-intercept = 6. Homework Equations The Attempt at a Solution

Friends: Recently I got this problem: what sustained horizontal wind pressure/force is needed to make a pendulum swing up and stay at a certain angle? To solve this problem, I imagined applying a horizontal force FH to the bob (of mass "m"). I learned that the angle that the pendulum makes...

Homework Statement What force have to be applied to stop an polymer object with mass 5 gram and velocity 0.1 mm/s to stop in 0.2 mm? The polymer object touches a human skin at one side only, whereby friction Ff has a influence in the stopping process. The object is moving to the left. In...

Homework Statement I'm having a lot of trouble trying to figure out this problem, any help would be great. The coefficient of static friction between a 3 Kg box and a 35 degree incline ramp is 0.3. What minimum force F perpendicular to the incline must be applied to the box to...

Homework Statement As the title says, the question asks of us to: Prove that the diagonals of a non square kite are perpendicular using vectors. Homework Equations if a is perpendicular to b then a . b =0 normal vector addition and subtraction The Attempt at a Solution a kite made...

Homework Statement Vectors find k if (4,1,k)τ & (5,1,-3)τ are perpendicular? From the answer sheet I know the answer is k = 7 Homework Equations I believe I need these two but I'm not certain: Dot-product: v*w = v1w1 + v2w2 + ... vdwd cos θ = v*w / ||v|| * ||w|| The Attempt at...

The other day, we were discussing cars going through turns and the max speed they could do without slipping. My teacher asked us if static or kinetic friction should be used. I answered static, because the wheels are rotating and thus not sliding over the road surface. He ended up saying the...

Homework Statement Let l1:x=3+t, y=1-t, z=2t and l2:x=-1+s, y=2s, z=1+kt (not sure if this one is just a typo, in which t should actually be s, or whether this is fundamental to the problem) be two lines in R3. a) Find all value(s) of k, (if any) for which l1 and l2 are parallel. If not...

how potential energy of electric dipole perpendicular to electric field is zero in this situation the torque is maximum so how P.E. can be zero please help

Homework Statement Distance from Earth to sun = 1.50 * 1011m Earth's orbital period = 3.16 * 107 s Distance from venus to sun = 1.08 * 1011m Venus's orbital period = 1.94 * 107 s Both orbits around the sun are coplanar, and the transit of venus about the sun is observed by a telescope on...

Homework Statement In the following diagram, the brown metallic conductor rod is given a slight push to the left. The black lines are all conducting wires, with the entire setup placed in a perpendicular B-field. Ignore friction. What will happen? 1) The rod slowly come to a stop? 2) The rod...

Homework Statement Given: P=(1,-2,3), Q=(-4,2,5) and S=(2,1-4) Find a unit vector that is perpendicular to triangle PQS Homework Equations Cross and Dot Product The Attempt at a Solution Correct me if I'm doing wrong. I have two solutions that I've thought: 1)What I...

Homework Statement A=(i+j-k) B=(2i-j+3k) Need to find vector perpenducilar to them Homework Equations The Attempt at a Solution I've solved by finding A*B and then divided it to (A*B), the result was W=2i/\sqrt{38}-5j/\sqrt{38}-3k/\sqrt{38}. Is it correct?

Homework Statement Let vector v=<1,-2, 6> and vector w=<30,-11, -2>. Represent vector w in the form of w=g+h, where g is parallel to v and h is perpendicular to v. Using the dot product Homework Equations The Attempt at a Solution I don't even know where to begin. I think...

Homework Statement A particle moves so that its pos. vector is gn by [FONT="Arial Black"]r = cos wt [FONT="Arial Black"]i+sin wt [FONT="Arial Black"]j. show that the velocity [FONT="Arial Black"]v of the particle is perpendicular to and that [FONT="Arial Black"]rx[FONT="Arial Black"]v is a...

Homework Statement Find the equation of the line perpendicular to Homework Equations −8y − 8 − 16x = 0 and passing through the point (18, 0). The Attempt at a Solution -8y = 16x +8 y = =2x -1 -2(x-18) = y - 0 -2x +36 = 0 -2 x = -36

Homework Statement I was a asked a question from an experiment: What happens if the light shone into the diffraction grating or a double slit is not perpendicular to the diffraction grating or double slit? What will happen?The Attempt at a Solution Straight away i can tell that the light...

Homework Statement A) Find the magnitude of the net magnetic field at point P and point Q B) Reverse the directon of the current for the wire on the x-axis Homework Equations B = μ0I/2πr The Attempt at a Solution Solution attempt attached. Only attempted part A, since I probably won't get...

Hello, I am trying to fit a sine function to a general curve. Convolution isn't giving me what I want, which is for every point on a general curve, displace that point by another function. I have written some code in Octave, and it's close, but not quite it. What I did was to take a general...

Given that a=(a1,a2,a3) and b=(b1,b2,b3) by applying the Pythagoras rule, Prove that a1b1+a2b2+a3b3=0 if a and b perpendicular The Scalar product a.b = |a||b|CosQ -------------(1) if two vectors are perpendicular; Q=90degrees then CosQ=0; from (1) a.b=0 (a1,a2,a3).(b1,b2,b3)=0 a1b1+a2b2+a3b3=0...

Homework Statement A pendulum bob of mass 2.5kg is pulled aside by a horizontal rope. If the tension in the rope is 3.50N, what is the angle between the pendulum and the vertical? mp = 2.5 kg Tr = 3.50 N Fg = 2.5kg * 9.8m/s2Homework Equations ∑F = 0 Pocket full of trig functions and...

Homework Statement If the acceleration/force vector is always perpendicular to the velocity vector, what is the path? Homework Equations F=ma a dot v=0 The Attempt at a Solution We know that the dot product of a and v is zero such that vx*vx'+vy*vy'=0 where vx'=dvx/dt...

Is amplitude always perpendicular to the rest axis? in a wavelength amplitude it the distance between either the crest or through from the equbilium line. then in the case of transverse vibration, what is its amplitude? thanks

Homework Statement If a curve has the property that the position vector r(t) is always perpendicular to the tangent vector r'(t), show that the curve lies on a sphere with center the origin. Homework Equations -1/r'(t)= slope of position vector x^{2}+y^{2}=1 The Attempt at a...

Homework Statement Vector p = i + j + k Vector q = 2i - j Find the perpendicular component of vector p of vector q. I think i have provided everything what is required, i just don't know what to find. I didn't get what the perpendicular compnent of vector p of vector q means...

Homework Statement A solenoid as viewed from the left has a current carrying wire wrapping around it counter clockwise. The current travels from left to right. The current varies as: I=I_0sin(wt) According to Faraday's law, this will result in electric field. From symmetry, the electric...

Homework Statement Two curves are perpendicular f(x)= x-4/x and h(x)= x+2/x^2-4x intersect at (2,-1). How would i find if they are perpendicular i first found the derivative of the equations by using the quotient rule but i do not know what to do next.

Homework Statement The lines r=(2+2t)i+(3-3t)j+(4-2t)k and v=(4+2s)i+(1-6s)j+(5-3s)k are skew. Find the perpendicular distance between them at the point(s) where they cross over each other. Homework Equations The Attempt at a Solution Does this seem right...

The line of intersection of two perpendicular planes is r=(-1+5t)i +(5-t)j +(7-4t)k. One plane is 5x-3y+7z=29. Find the rectangular equation of the other plane. The Attempt at a Solution I think I need to find three points in the desired plane. (one point being (-1,5,7)?)

Homework Statement Find the slope of the line through x(2, -3) and y(1, 2). What is the slope of any line perpendicular to xy? Hence, find the equation of the line through the origin and which is perpendicular to xy. Homework Equations slope formula: m = y2 - y1/ x2 - x1...

Hi, one of my vac work questions is: A lamina has density d(x,y) = x^2 + y^2 and is defined by -2<x<2 ; -3<y<3. Calculate the moment of inertia about an axis perpendicular to the lamina through the point (1,1). I'm confident that I find Ix which is equal to the double integral of the...

Homework Statement Determine value of k when thehse are perpendicular: [x,y,z] = [1+4s+kt, 2+2s+t, 7+2t] and [x,y,z] = [4,1,-1] + s[1,0,5] + t[0,-3,3] The Attempt at a Solution I learned that in 2 and 3D, two lines are perpendicular only if, after solving for the t in front of the...

"If u and v are any two vectors of the same length, use the dot product to show that u + v is perpendicular to u − v. What fact from geometry is does this represent." This is basically the last question in an assignment on vectors (first year university, linear algebra). The questions all focus...

Homework Statement ABCD is a quadrilateral with AB=CD P,Q,R,S are the midpoints of AD,AC,BD,BC respectively Prove that PS is perpendicular to QR Homework Equations The Attempt at a Solution I've tried a bunch of different avenues, but I think that the most promising one is...

Homework Statement Determine the coordinates of the points on the graph of f(x) = _/'2x+1 where the tangent line is perpendicular to the line 3x+y+4 = 0 _/' -means square root Homework Equations f(x) = _/'2x+1 3x+y+4 = 0 The Attempt at a Solution I made it equal to y like y= -3x-4...do I...