Q 47.

Question

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

Step-by-Step Solution

Verified

Answer

The required vector is $\frac{7}{\sqrt{53}} <1, 4, 6>$ .

1Step 1. Given information.

The given vector is:

$v = <- 1, - 4, - 6>$ with magnitude 7.

2Step 2. Find the norm of the vector.

$v = <- 1, - 4, - 6> ||v|| = \sqrt{{(- 1)}^{2} + {(- 4)}^{2} + {(- 6)}^{2}} = \sqrt{1 + 16 + 36} = \sqrt{53}$

Therefore, the norm of the given vector is $\sqrt{53}$ .

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 $v = <- 1, - 4, - 6>$ .

The required vector is:

$\frac{a}{||v||} (- v) = \frac{7}{\sqrt{53}} (- <- 1, - 4, - 6>) = \frac{7}{\sqrt{53}} <1, 4, 6>$

Therefore the vector in the direction opposite to $v = <- 1, - 4, - 6>$ and with a magnitude of 7 is $\frac{7}{\sqrt{53}} <1, 4, 6>$ .

Q 46.

Q 48.

Other exercises in this chapter

Q 45.

Find a vector in the direction of 8,-7,2 and with magnitude 2.

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Q 46.

Find a vector in the direction of 9,0,-6 and 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 49.

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

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