Question

Vector question:
a=2i+6j+10k
b=4i+7j=2k
Find two vectors u and v such that:
v is perpendicular to a
u is parallel a
b=u+v

Answer 1

v perpendicular to a, v.a = 0

u parallel to b , u = k(b) ... you can easily construct a vector ... is that last equation is also a requirement?

Answer 2

sorry u = k(a)

Answer 3

let

Answer 4

v = xi+yj+zk, then 2x+6y+10z = 0, ----1
4i+7j-2k = xi+yj+zk + k (2i+6j+10k) --- 2

compare the coefficients on 2, put the value of x,y,z on 1 (in terms of k), find the value of k, and back to 2, find x, y, z

Answer 5

i leave the rest of work to you

Answer 6

ok thanks for your help