find a vector that has the same direction as (-2, 4, 2) but has length 6?

Question

thanks

Answer 1

find unit vector in direction of (-2,4,2) by dividing by the length, √(4 + 16 + 4) = √24 = 2√6, then multiply by 6, so you have 6/(2√6)[-2,4,2] = (3/√6)[-2,4,2] = [-6/√6, 12/√6, 6/√6].

if you don't like irrational denominators, rationalize as [-√6, 2√6, √6].

Answer 2

divide your vector by its magnitude then multiply it this time by 6.

dividing any vector by its magnitude makes it a unit vector, a vector of length 1.