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

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

Let's understand the solution in detail.

**Explanation:**

Given:

A_{0} = (−6, 4, 6).

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

Thus, A_{1} = (−6u, 4u, 6u)

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

Given that length should be 6:

⇒ u⋅√88 = 6

⇒ u = 6 / √88

⇒ u = 6 / 2√22

⇒ u = 3/√22

Substituting the value of 'u' back to A_{1} we get,

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

A_{1} = (−18/√22, 12/√22, 18/√22)

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

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