# Find a vector that has the same direction as (−6, 4, 2) but has length 6.

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

## Answer: A vector with the same direction as (−6, 4, 2) but has length 6 is (−18/√14, 12/√14, 6/√14).

Let's solve this step by step.

**Explanation:**

Given, \(A_{0}\) = (−6, 4, 2)

Let \(A_{1}\) be the vector in the same direction as \(A_{0}\) but with length 6: \(A_{1}\) = (−6u, 4u, 2u).

The length of a vector with coordinates (−6u, 4u, 2u) is equal to √(36 u^{2} + 16 u^{2} + 4 u^{2}) = u × √56

Given that length should be 6.

⇒ u × √56 = 6

u = 6 / 2√14 = 3/√14

\(A_{1}\) = (−6 × 3/√14, 4 × 3/√14, 2 × 3/√14)

\(A_{1}\) = (−18/√14, 12/√14, 6/√14)