Chapter 10: Q 50. (page 801)

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

Short Answer

Expert verified

The required vector is $\frac{1}{\sqrt{50}} <- 3, - 4, - 5>$ .

Step by step solution

Step 1. Given information.

The given vector is:

$v = <3, 4, 5>$

Step 2. Find the norm of the vector.

$v = <3, 4, 5> ||v|| = \sqrt{3^{2} + 4^{2} + 5^{2}} = \sqrt{9 + 16 + 25} = \sqrt{50}$

Therefore, the norm of the given vector is $\sqrt{50}$ .

Step 3. Find the vector.

We know that the vector in the direction of vis $\frac{1}{||v||} (- v)$ . Here ais the magnitude of the given vector and the negative sign shows the direction opposite to $v = <3, 4, 5>$ .

The required vector is:

role="math" localid="1649521227299" $\frac{1}{||v||} v = \frac{1}{\sqrt{50}} (- <3, 4, 5>) = \frac{1}{\sqrt{50}} <- 3, - 4, - 5>$

Therefore, the unit vector in the direction opposite to $v = <3, 4, 5>$ is $\frac{1}{\sqrt{50}} <- 3, - 4, - 5>$ .

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

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 unit vector in the direction opposite to3,4,5.

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

Probability and Statistics

Geometry

Mechanics Maths

Decision Maths

Discrete Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

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