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

Vectors are very interesting concepts in mathematics that have an immense number of applications in engineering and physics. They have many interesting properties. We will be using the concept of scaling and the similarity of the vectors.

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

Let's solve this step by step in detail.

**Explanation:**

Given, A_{0} = (−6, 6, 4)

Let A_{1} be the vector in the same direction as A_{0} but with a length of 6

Hence A_{1} = (−6u, 6u, 4u)

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

Given that length should be 6

⇒ u⋅√88 = 6

⇒ u = 6 / √88

⇒ u = 6 / 2√22

⇒ u = 3/√22

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

A_{1} = (−18/√22, 18/√22, 12/√22)

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

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