Question

Find a vector w with the same direction of u but twice as long as v. u = {0 4 2} v = {2 1 0}. I did some caculate, but I think I am wrong.

I done the length of v is
√5
, unit vector with the same direction of u is
0,2/√5,1/√5
, but I think if w has same direction and twice long as v (2*√5) it will be {0 4 2}, same as u,

am I wrong??

Answer 1

how about getting a unit vector in the same direction as u?

Answer 2

- find magnitude of v and then double it
- find unit vector of u
- multiply the above two

Answer 3

- magnitude of v and then double it
\[magnitude ||v|| = \sqrt{2^2 + 1^2 + 0^2} = \sqrt{5}\]
double it become
\[2\sqrt{5}\]
- find unit vector of u
\[magnitude ||u|| = \sqrt{0^2 + 4^2 + 2^2} = 2\sqrt{5}\]

so \[unit.vector = \left\{ 0, \frac{ 2 }{ \sqrt{5} }, \frac{ 1 }{ \sqrt{5} } \right\}\]

- multiply the above two
result is {0, 4, 2} same as u, am I wrong?

Answer 4

when u multiply u get ( 0, 4/5, 2/5)

Answer 5

you are correct in your solution, @ccclp