Chapter 9: Q. 49 (page 622)

In Problems 45–50, find the unit vector in the same direction as v.
$v = i + j + k$

Short Answer

Expert verified

The unit vector in the same direction as $v = i + j + k$ is $\frac{\sqrt{3}}{3} i + \frac{\sqrt{3}}{3} j + \frac{\sqrt{3}}{3} k$

Step by step solution

Step 1. Given

The vector $v = i + j + k$

To find the unit vector.

Step 2. Unit vector in the direction of v

For any nonzero vector v, the vector $u = \frac{v}{||v||}$ is a unit vector that has the same direction as v.

Step 3. Find v

Now,

$||v|| = ||i + j + k|| = \sqrt{1^{2} + 1^{2} + 1^{2}} = \sqrt{3}$

Step 4. Find the unit vector.

The unit vector is,

$u = \frac{v}{||v||} = \frac{i + j + k}{\sqrt{3}} = \frac{\sqrt{3} i + \sqrt{3} j + \sqrt{3} k}{3} = \frac{\sqrt{3}}{3} i + \frac{\sqrt{3}}{3} j + \frac{\sqrt{3}}{3} k$

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In Problems 45–50, find the unit vector in the same direction as v.
$v = i + j + k$

Short Answer

Step by step solution

Step 1. Given

Step 2. Unit vector in the direction of v

Step 3. Find v

Step 4. Find the unit vector.

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In Problems 45–50, find the unit vector in the same direction as v.v=i+j+k

Short Answer

Step by step solution

Step 1. Given

Step 2. Unit vector in the direction of v

Step 3. Find v

Step 4. Find the unit vector.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Calculus

Geometry

Applied Mathematics

Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In Problems 45–50, find the unit vector in the same direction as v.
$v = i + j + k$