Chapter 10: Q 47. (page 801)

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

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information.

The given vector is:

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

Step 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 $\sqrt{53}$ .

Step 3. Find the vector.

We know that the vector in the direction of vis $\frac{a}{||v||} (- v)$ . Here ais 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 $\frac{7}{\sqrt{53}} <1, 4, 6>$ .

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

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the norm of the vector.

Step 3. Find the vector.

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

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the norm of the vector.

Step 3. Find the vector.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Mechanics Maths

Theoretical and Mathematical Physics

Calculus

Decision Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

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