Question

How do you find the unit vector having the same direction as vector v = 2i - j + k?

Answer 1

The unit vector having the same direction as `v` will be `2/sqrt6i-1/sqrt6j+1/sqrt6k`

Explanation:

For a vector `v=ai+bj+ck`, unit vector in the same direction is given by `v/(|v|)`, where `|v|=sqrt(a^2+b^2+c^2)`.

Hence for `v=2i-j+k`, as `|v|=sqrt(2^2+(-1)^2+1^2)`

= `sqrt(4+1+1)=sqrt6`

Hence. the unit vector having the same direction as `v` will be

`2/sqrt6i-1/sqrt6j+1/sqrt6k`