# Find a vector that has the same direction as (−4, 6, 6) but has length 6.

We will be using the concept of scaling and the similarity of the vectors.

## Answer: A vector that has the same direction as (−4, 6, 6) but has length 6 is (−12/√22, 18/√22, 18/√22).

Let's solve this step by step.

**Explanation:**

Given, A_{0} = (−4, 6, 6)

Let A_{1} be the vector in the same direction as A_{0} but with length 6: A_{1} = (−4u, 6u, 6u)

The length of a vector with coordinates (−4u, 6u, 6u) is equal to √(16 u^{2} + 36 u^{2} + 36 u^{2}) = u ⋅ √88

Given that length should be 6:

⇒ u ⋅ √88 = 6

u = 6 / 2√22 = 3/√22

A_{1} = (−4 × 3/√22, 6 × 3/√22, 6 × 3/√22)

A_{1} = (−12/√22, 18/√22, 18/√22)