Question

Find a unit vector that has the same direction as the given vector. −6i + 2j − k

Answer 1

The unit vector with the same direction of the vector v = - 6 i + 2 j - k is u = - (6√41 / 41) i + (2√41 / 41) j - (√41 / 41) k.

How to determine the unit vector

Vectors are characterized both by magnitude and direction, unit vectors are vectors with a magnitude of 1. Then, the unit vector can be found by the following formula:

u = v / ||v||      (1)

Where:

• ||v|| - Norm of the vector
• v - Vector

The norm of the vector can be determined by Pythagorean theorem. Then, we find the unit vector:

||v|| = √[(- 6)² + 2² + (- 1)²]

||v|| = √41

u = (- 6 i + 2 j - k) / √41

u = - (6 / √41) i + (2 / √41) j - (1 / √41) k

u = - (6√41 / 41) i + (2√41 / 41) j - (√41 / 41) k

The unit vector with the same direction of the vector v = - 6 i + 2 j - k is u = - (6√41 / 41) i + (2√41 / 41) j - (√41 / 41) k.

To learn more on unit vectors: brainly.com/question/28028700

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