Q 49.

Question

Find a vector in the direction opposite to $<0, - 3, 4>$ and with magnitude 10.

Step-by-Step Solution

Verified

Answer

The required vector is $2 <0, 3, - 4>$ .

1Step 1. Given information.

The given vector is:

$v = <0, - 3, 4>$ with magnitude 10.

2Step 2. Find the norm of the vector.

$v = <0, - 3, 4> ||v|| = \sqrt{0^{2} + {(- 3)}^{2} + 4^{2}} = \sqrt{0 + 9 + 16} = \sqrt{25} = 5$

Therefore, the norm of the given vector is 5.

3Step 3. Find the vector.

We know that the vector in the direction of v is $\frac{a}{||v||} (- v)$ . Here a is the magnitude of the given vector and the negative sign shows the direction opposite to $v = <0, - 3, 4>$ .

The required vector is:

$\frac{a}{||v||} (- v) = \frac{10}{5} (- <0, - 3, 4>) = 2 <0, 3, - 4>$

Therefore the vector in the direction opposite to $v = <0, - 3, 4>$ and with a magnitude of 10 is $2 <0, 3, - 4>$ .

Q 48.

Q 50.

Other exercises in this chapter

Q 47.

Find a vector in the direction opposite to-1,-4,-6and with magnitude 7.

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Q 48.

Find a vector in the direction opposite to -4,5,-1 and with magnitude 3.

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Q 50.

Find a unit vector in the direction opposite to 3,4,5.

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Q 51.

Find a vector of length 3 that points in the direction opposite to 1,-2,3.

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