Vector algebra Definition and 74 Threads

Homework Statement I'm having difficulty showing that the general equation k = 2∏/λ holds from the component equations kx = 2∏/λx etc..., k = √(kx2 + ky2 + kz2), and λ = √(λx2 + λy2 + λz2). Any help? There is a photo from a textbook with the equations also below. Homework Equations...

Homework Statement Two beetles run across flat sand, starting at the same point. Beetle 1 runs 0.50m due east, then 0.80m at 30° north of due east. Beetle 2 also makes two runs; the first is 1.6m at 40° east of due north. What must be (a) the magnitude and (b) the direction of its second run...

Homework Statement A unit cell of diamond is a cube of side A, with carbon atoms at each corner, at the centre of each face and, in addition, at positions displaced by 0.25A(i + j + k) from each of those already mentioned; i, j, k are unit vectors along the cube axes. One corner of the cube...

1. An air ambulance is traveling from Barrie to Toronto. Toronto is located 90 km (S 5° E) of Barrie. If the wind is blowing from the South with a velocity of 62 km/h, and the plane's air speed is 375 km/h, what direction must the pilot fly to make it to Toronto? 2. Let u=<u_{1},u_{2}>...

I need general help with vector algebra. Is there a FAQ, tutorial, or section of the forums here that I should look at?

Homework Statement P is the point where the diagonals of the parallelogram abcd intersect one another let \alpha = AB and \beta = AD and let s and t be scalars such that AP = sAC and BP = tBD use vector algebra to show that s(\alpha + \beta) = AP = \alpha + t(\beta - \alpha)The Attempt at...

where x represents cross product currently if i forget i figure these out using the right hand rule, but how do you get each equation visa versa using vector algebra i started with w = rxv how do you derive that v = wxr i got up to this w = rxv w= -(vxr) rxw = -rx(vxr) rxw =...

Homework Statement Let V be a vector space over the field F. Define what is meant by the statement "For vectors v1, v2,...,vn belonging to V, the set {v1,v2,...,vn} spans V Homework Equations None The Attempt at a Solution Does it mean that the set is linearly dependent?

Homework Statement Velocity vector for a .5kg body, t=1s to t=35s, is v=5t^2 i + 3/t j – t k WHat is the position vector? what is the angular momentum vector?what is the acceleration vector? what is torque exerted on the body? Homework Equations L=rxp=rxmv T=rxf=rxma The Attempt at...

Homework Statement Find the parametric equations for the line which passes through the point (3,5,7) and parallel to the vector <2,6,8>. Is the line perpendicular to the plane 5x + 6y +7z = 10? Homework Equations line equation, r = Ro + tV The Attempt at a Solution line...

Homework Statement Prove, by writing out in component form, that \left(a \times b \right) \times c \equiv \left(a \bullet c\right) b - \left(b \bullet c\right) aand deduce the result, \left(a \times b\right) \times c \neq a \times \left(b \times c\right), that the operation of forming the...

p = (2,6,3) q = (1,0,1) r = (4,1,-1) part a) Find a parametric equation of the line that passes through p with direction q x=p + t(q) x=(2,6,3) + t(1,0,1) part b) find the point X on the line in part a so that RX is perpendicular to the line I'm having trouble doing this one...

Homework Statement line l1 : x=2 y= -1 + p z= 2p line l2 : x=-1 + t y=1-3t z=1-2t Find the shortest (exact) distance between l1 and l2. Homework Equations That's what I am looking for! The Attempt at a Solution Thanks!

Homework Statement A ball of mass 1 kg is acted upon by three forces: Fl = (2i + 4j - 3k) N, F2 = (-3i - j + 2k) Nand F3 = (i - 5j - k) N. Determine a vector expression for the acceleration of the particle. If, at time t = 0, it has position r = (i +j) m and velocity u = (i +3j)m/s...

Hi everyone. I am not sure if this problem belongs under the "Linear & Abstract algebra" section but it seemed like it may. Please let me know if there is a different section that would better fit this problem. So here is a word problem that is proposed: A solar panel is capable of rotating...

Dear all, Anyone happan to have good online lecture video links on Vector Algebra? I need to get an understanding of things like 'Curl', 'Divergence' etc which I will be using it for my Electromagnetic module. Any help/advise will be greatly appreciated. Thanks in advance. Regards

Homework Statement a(v), b(v) and c(v) are three vectors. if a(v) x b(v) = c(v) and b(v) x c(v)= a(v) Show that b(mod)= 1 and a(mod)=c(mod) and the three vectors are mutually perpendicular. (v) denotes vector and (mod) denotes magnitude. [b]2. Homework Equations [/] NA. The Attempt...

Complex four vector spacetime algebras in relativity Does anyone have any experience or references as to the usefulness and applicability of this in relativity?

Please can somebody help me to find video tutorials or e-books for these

Can somebody tell me where I can find these e-books.please help me.Thank you all

Hello all. Happy to have finally found this forum, sorry that it took so long! I'm working through a Vector Algebra tutorial and I am having much difficulty with the concepts of Kronecker deltas and the Levi-Civita symbol. I can't fully grasp either of them intiutively. From what I've been...

Okay here is my work: http://show.imagehosting.us/show/891312/0/nouser_891/T0_-1_891312.jpg and here is my calculations part: http://img136.imageshack.us/img136/5539/lastscan7qc.jpg Problem says: 14. [HRW7 28.P.008.] An electron has an initial velocity of (14.0 j + 21.0 k) km/s and a...

hello, I'm taking electrodynamics, and to begin we're doing vector algebra/calculus. here's the problem I'm faced with. there's a triangle defined by the points. (1,0,0) (0,2,0) (0,0,3) the task at hand is finding the unit vector orthogonal to the defined plane. the method that...

I hate Vector Algebra! I am having some trouble doing some vector algebra and any help or direction is greatly appreciated. In our lecture we drew a vector C(s) = A + s(B-A) which described a line passing through points A and B and found that the vector of min. length (shortest dist. from...