# Find a vector that has the same Direction as (−6, 6, 2) 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 (−6, 6, 2) but has length 6 is (−18/√19, 18/√19, 6/√19).

Let's solve this step by step.

**Explanation:**

Given, \(A_{0}\) = (−6, 6, 2)

Let \(A_{1}\) be the vector in the same direction as \(A_{0}\) but with length 6: \(A_{1}\) = (−6u, 6u, 2u)

The length of a vector with coordinates (−6u, 6u, 2u) is equal to √(36 u^{2} + 36 u^{2} + 4 u^{2}) = u ⋅ √76

Given that length should be 6.

⇒ u ⋅ √76 = 6

u = 6 / 2√19 = 3/√19

\(A_{1}\) = (−6 × 3/√19, 6 × 3/√19, 2 × 3/√19)

\(A_{1}\) = (−18/√19, 18/√19, 6/√19)

### Hence, a vector that has the same direction as (−6, 6, 2) but has length 6 is (−18/√19, 18/√19, 6/√19).

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