Question

Find the vector that has the same direction as 3, 6, −2 but has length 5.

Answer 1

√(3² + 6² + (-2)²) = √(9 + 36 + 4) = √49 = 7

(5/7)(7) = 5, so we have:

3(5/7) = 15/7, 6(5/7) = 30/7, -2(5/7) = -10/7

The vector (15/7, 30/7, -10/7) has the same direction as (3, 6, -2) and has length 5.