I have always seen YouTube videos saying how an electron 'knows' when we are observing it but I always put that down to youtubers creating popular science (verging on science fiction) hype for more views. I suppose there is more science behind an electron behaving like a particle when we put a...
Hello,
I'm an Indian student just graduating from high school and am about to begin studies in Memorial University of Newfoundland. I'm not sure whether to pursue a computer science degree or a computer engineering degree- I'm fascinated by AI and have learned a bit of coding myself, any...
Good day everyone, I'm an Indian student about to complete high school and I've applied for computer engineering in Memorial University of Newfoundland, Canada. My class 10th GPA is 9.6 and I am expecting at least 85% in class 12th boards. This year the JEE (Indian SATs for engineering) was also...
Good day everyone, I'm an Indian student about to pass out from high school- The competition here is intense for the few truly good engineering colleges here so I'm looking for some guidance to studying in Canadian universities. I'd really appreciate your help- Thank you.
a) I am expecting a...
Homework Statement
I noticed that for a line parallel to z axis the equation is (x-a)/0 = (y-b)/0 = (z-c)/k = t.
Homework Equations
Any 3d geometry equations
The Attempt at a Solution
I can't quite grasp how to visualize this, also I can't see any constant like a 2d line parallel to x axis...
Homework Statement
a source of sound of frequency f emits sound with speed v, is at rest. If an observer is moving at towards source with speed u, then wavelength of sound waves observed by the observer will be?
Homework Equations
f' = f(u+v)/u...(i) f' is apparent frequency, f is the real...
Homework Statement
If the plane 3x+y+2z+6=0 is parallel to the line (3x-1)/2b = 3-y = (z-1)/a then 3a+3b is?
Homework Equations
angle between two lines=90 degree when l1l2+m1m2+n1n2=0 where l,m,n are direction ratios...(i)
The Attempt at a Solution
First I divided x/3 and 3-y by -1 to get the...
Homework Statement
A vector n of magnitude 8 units is inclined to x,y and z axis at 45, 60 and 60 degrees resoectively.If the plane passes through (root2, -1, 1) and is normal to n then find its equation.
Homework Equations
(r-a).n=0 where r is position vector of a point on plane, a is a point...
Homework Statement
Find equation of line of intersection of planes r.(3i-j+k)=1 and r.((i+4j-2k)=2
Homework Equations
a x b gives a perpendicular vector to a and b...(i)
The Attempt at a Solution
to write equation of a line r=a+tb we need a point a on the line and a parallel vector b. Taking...
Homework Statement
Consider three equations in three variables, To check their consistency usually the adjoint of the matrix (from coefficients of x,y and z are found) and the inverse is found for the solution. I have heard of cramer's rule but it has a similar complexity.
These same kind of...
Homework Statement
I read in my textbook that the force exerted by a charged particle q1 on another charged particle q2 does not depend on the medium between them. Yet we multiply ε by ε(r) in coulomb's law when there is a medium present between the particles. Can someone please explain this...
Homework Statement
Find the value of z for which (10x-5)^2 + (10y-7)^2 = z^2((5x+12y+7)^2 is a parabola
Homework Equations
eccentricity of parabola=1
The Attempt at a Solution
I can solve this by expanding everything and writing h^2-ab=0 but this equation looks suspiciously similar to...
Homework Statement
The operating cost of a truck is 12+(x/6) per km, when the truck travels x km/hr. If the driver earns 6 rupees (*or whatever currency your country has) per hour, what is the most economic speed to operate the truck on a 400 km road? Also, due to weather, the truck can travel...
Homework Statement
## \lim x-a \frac {{a^x-{x^a}}}{{x^x}-{a^a}} = -1## then a is?
Homework Equations
L'Hospital rule
The Attempt at a Solution
Using LHR we can write numerator as ##\frac{a^x ln{a}-ax^{a-1}}{x^xln(x+1)}##
plugging x=a and equating to -1 gives 1-ln(a)=ln(a+1); so 1=ln(a(a+1))...
Homework Statement
## \lim x-0 \frac {xcosx-log(1+x)}{x^2}##
Homework Equations
##\frac{log(1+x)}{x}=1## ...(i)
The Attempt at a Solution
Using (i) we can write numerator as xcosx-x, cancelling x from denominator we have cosx-1/x, this is 0/0 form so we can use LHR which gives us -sinx/1 but...
Homework Statement
lim x--->0 |x|^sinx is?
Homework Equations
lim x-->0 f(x)^g(x), if both functions tend to 0, limit is equal to e^log[f(x).g(x)] with the same limit..(i)
The Attempt at a Solution
when x>0, it is x^sinx and x<0 it is -1/x^sinx. putting the first case in (i) we get...
Homework Statement
how to write the vector equation of the line of shortest distance between two skew lines in the shortest and most efficient way?
(The exact lines given in a particular problem in my book can be referenced- L1=(3i+8j+3k)+λ(3i-j+k) and L2=(-3i-7j+6k)+μ(-3i+2j+4k) )
2. Relevant...
Homework Statement
Find the coordinates of those points on the lines (x+1)/2 = (y+2)/2 = (z-3)/6 which is at a distance of 3 units from the point (1,-2,3)
2. Relevant methods
1) assume a point, use distance formula- (very calculative)
2) write vector equation of line, find foot of...
Homework Statement
Suppose a line is given, say (x-3)=(y-2)=z in Cartesian form and we are supposed to find a point on it which is at a distance say, 6 units from a given arbitrary point (1,2,3).
2. Relevant tedious methods
1) write line in vector form then equate modulus of vector between...
Homework Statement
A vector r has length 21 and direction ratio's 2,-3,6. The direction cosines of r, given that r makes an obtuse angle with x axis is given by?
Homework Equations
l/a = m/b =n/c ...(1) (l,m,n are direction cosines, a,b,c are direction ratios
l^2 + m^2 + n^2=1....(2)
The...
Homework Statement
A line makes some angle T with each of x and z axis, and angle U with y axis so that sin^2(U)=3sin^2(T).
Homework Equations
2cos^2(T)+cos^2(U)=1 .......(i)
cos^2(x)+sin^2(x)=1
The Attempt at a Solution
Using the above two eqns. give us the correct value for cos^2(T) which is...
Homework Statement
If magnitudes of vector a,b and c are 1,2,3 respectively and vectors a+b+c=0 then it is obvious that a and b will be in the opposite direction to c therefore cancelling it out but let's assume for a moment that we don't know this and we want to figure this out using the sine...
Homework Statement
Equation of the circle passing through the point (1,2) and (3,4) and touching the line 3x+y-3=0 is?
Homework Equations
x^2+y^2+2gx+2fy+c=0...(1)
(-g,-f)=center of circle
sqrt(g^2+f^2-c)=radius...(2)
The Attempt at a Solution
Putting (1,2) and (3,4) in equation 1 we get...
Homework Statement
A thin convex lens of focal length 20 cm is split into two parts along the principal axis, now there is a 2mm gap between the top and bottom parts, an object O is placed at 10 cm from the lens, the distance between the two virtual images will be?
Homework Equations
1/v - 1/u...
Homework Statement
My question is, are real images always inverted and virtual always erect?
Homework Equations
1/v+1/u=1/f for mirrors
and 1/v-1/u=1/f for lenses
The Attempt at a Solution
Consider a concave lens, with object at -x. the condition for a virtual image is v<0; i.e on the same...
Homework Statement
In a given square ABCD each side is of 1 m and resistance of wire is 1 ohm/m. A resistance of 1 m is connected from A to E (which lies on side CD). A constant potential difference is applied across A and C, if potentials of B and E are same then find CE/ED.
Homework...
Homework Statement
The following figure shows a circuit containing a bulb, switch and battery. Four voltmeters are connected in it to measure potential difference. Which voltmeters give non-zero readings and which ones read terminal potential difference when the switch is 1) open and 2) closed...
Homework Statement
In the given circuit at t=0 S is closed then at time t, i1/i2 a) is constant b) increases c) decreases d) first increases then decreases
Homework Equations
V=IR, Q=CV
The Attempt at a Solution
At t=0, capacitors act like closed switches, so I2=2I1, where I2 and I1 are the...
Homework Statement
In the circuit shown, C1= 1 microfarad, C2=3 microfarad, in steady state, the energy stored in these capacitors are?
Homework Equations
Kirchoff's laws, E=0.5CV^2, V=IR
The Attempt at a Solution
At steady state, no current passes through the capacitors, so current is...