Find a vector that has the same direction as the given vector but has length 6.

Question

‹-2, -2, 4›

I know how to find a unit vector of this, but to find a vector in the same direction but length >1 I'm not sure how to determine the scalar multiple that will be needed. I know it will be >1 because the length of the current vector is sqrt(24) and l=6 would be l=sqrt(36).

I tried using the multiple of sqrt(36/24) but it didn;t work.

Any help would be appreciated.'

Answer 1

a vector with the same direction is (-1,-1,2)
a unit vector in that same direction is
1/√6(-1,-1,2) or (-1/√6, -1/√6, 2/√6)

so a vector 6 times that long is (-6/√6, -6/√6, 12/√6)
or
(-√6 , -√6 , 2√6) after rationalizing the denominator.