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# 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)

### Hence, a vector with the same direction as (−4, 6, 6) but has length 6 is (−12/√22, 18/√22, 18/√22).

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