Question

Vector u has initial points at (21,12) and it’s terminal point at (19,-8). Vector v has a direction opposite that of u. Who’s 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?

Answer 1

The correct form of vector v expressed as a linear combination of the unit vectors i and j is $\vec v = 10\,\hat{i} + 100\,\hat{j}$.

What is the value of a vector with respect to another vector?

First, we need to determine the value of the vector u by subtracting two vectors whose initial points are at the origin:

$\vec u = (19\,\hat{i} - 8\,\hat{j}) - (21\,\hat{i} + 12\,\hat{j})$

$\vec u = - 2\,\hat{i} - 20\,\hat{j}$     (1)

According to the statement, vector v is antiparallel to vector u and its magnitude is five times as the magnitude of vector v, which means that (1) must be multiplied by two scalars:

$\vec v = - 1 \,\cdot \, 5\cdot \vec u$      (2)

Please notice that antiparallelism is represented by the scalar - 1, whereas the dilation is represented by the scalar 5.

$\vec v = 10\,\hat{i} + 100\,\hat{j}$

The correct form of vector v expressed as a linear combination of the unit vectors i and j is $\vec v = 10\,\hat{i} + 100\,\hat{j}$.

Remark

The statement presents typing mistakes, correct form is shown below:

Vector u has initial points at (21, 12) and its terminal point at (19, - 8). Vector v has a direction opposite that of u, whose magnitud is five times the magnitud of v. Which is the correct form of vector v expressed as a linear combination of the unit vectors i and j?

To learn more on vectors: brainly.com/question/13322477

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