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# Find a unit vector that has the same direction as the given vector: (−8, 4, 8).

Vectors have many applications in the field of engineering and physics. Many problems related to kinematics and laws of motion are solved by using vectors.

## Answer: A unit vector with the same direction as (−8, 4, 8) is (−2/3, 1/3, 2/3).

Let's solve this step by step in detail.

**Explanation:**

Given, A_{0} = (−8, 4, 8)

Let A_{1} be the unit vector in the same direction as A_{0}

Hence, A_{1} = (−8u, 4u, 8u)

The length of a above vector is given by √[(-8)^{2} u^{2} + 4^{2} u^{2} + 8^{2} u^{2}] = u ⋅ √144 = 12u

Since, we have to find the unit vector, the length should be equal to one:

⇒ 12u = 1

u = 1/12

A_{1} = (−8 × 1/12, 4 × 1/12, 8 × 1/12)

Simplifying the above vectors, we get:

A_{1} = (−2/3, 1/3, 2/3)

### Thus, a unit vector with the same direction as (−8, 4, 8) is (−2/3, 1/3, 2/3).

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