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

Let's solve this step by step.

**Explanation:**

Given, \(A_{0}\) = (−2, 4, 2)

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

The length of a vector with coordinates (−2u, 4u, 2u) is equal to √(4 u^{2} + 16 u^{2} + 4 u^{2}) = u ⋅ √24

Given that length should be 6:

⇒ u ⋅ √24 = 6

u = 6 / 2√6 = 3/√6

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

\(A_{1}\) = (−√6, 2√6, √6)