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umka21 [38]
2 years ago
11

Im not sure how to answer this question.

Mathematics
1 answer:
bonufazy [111]2 years ago
3 0

9514 1404 393

Answer:

  (-4√494)/13i +(6√494)/13k ≈ -6.8388i +0j +10.2585k

Step-by-step explanation:

To answer this question, you need to know two things:

  1) the direction of vector v

  2) the magnitude of vector u

__

<u>direction of v</u>

A direction is specified by a "unit vector", one with the proper ratio of components, and a magnitude of 1. It is found from a given vector by dividing that vector by its magnitude.

The unit vector in the v direction is ...

  v/|v| = (-2i +3k)/(√((-2)² +3²) = (-2i +3k)/√13

__

<u>magnitude of u</u>

The magnitude of vector u is ...

  |u| = √(5² +(-2)² +3²) = √38

__

Then the desired vector is ...

  (2|u|)(v/|v|) = 2√38(-2i+3k)/√13 = (-4√494)/13i +(6√494)/13k

_____

<em>Additional comment</em>

We have chosen to "rationalize the denominator" by writing √(38/13) as (√494)/13.

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