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mrs_skeptik [129]
3 years ago
7

Vector u has its initial point at (21, 12) and its terminal point at (19, -8). Vector v has a direction opposite that of u, whos

e magnitude is five times the magnitude of v. Which is the correct form of vector v expressed as a linear combination of the unit vectors i and j?
Mathematics
1 answer:
ohaa [14]3 years ago
3 0

\boxed{\vec{v}=\frac{2}{5}i+4j}

<h2>Explanation:</h2>

In this exercise, we have the following facts for the vector \vec{u}:

  • It has its initial point at (21,12), let's call it P_{1}
  • It has its terminal point at (19,-8), let's call it P_{2}

Since the vector \vec{u} goes from point P_{1} to P_{2}, then:

\vec{u}=(19,-8)-(21,12) \\ \\ \vec{u}=(19-21,-8-12) \\ \\ \vec{u}=(-2,-20)

On the other hand, we have the following facts for the vector \vec{v}:

  • Vector \vec{v} has a direction opposite that of \vec{u},
  • The magnitude of \vec{u} is five times the magnitude of v.

So we can write this relationship as follows:

5\vec{v}=-\vec{u} \\ \\ \vec{v}=-\frac{1}{5}\vec{u} \\ \\ \vec{v}=-\frac{1}{5}(-2,-20) \\ \\ \vec{v}=(\frac{2}{5},4) \\ \\ \\ Finally: \\ \\ \boxed{\vec{v}=\frac{2}{5}i+4j}

<h2>Learn more:</h2>

Length of vectors: brainly.com/question/12264340

#LearnWithBrainly

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