Chapter 9: Q. 47 (page 603)

Find the unit vector in the same direction as $v$ .
role="math" localid="1646752725885" $v = 5 i$

Short Answer

Expert verified

The unit vector in the same direction as $v$ is $i$ .

Step by step solution

Step 1. Given information.

Consider the given question,

$v = 5 i$

The magnitude of the vector $v = a_{1} i + b_{1} j$ ,

$||v|| = \sqrt{{(a_{1})}^{2} + {(b_{1})}^{2}}$

Compare $v = 5 i$ with the standard form $v = a_{1} i + b_{1} j$ ,

$a_{1} = 5, b_{1} = 0$

Thus,

$||v|| = \sqrt{5^{2} + 0^{2}} ||v|| = 5$

Step 2. Find the unit vector.

Consider the given question,

The unit vector in the same direction as any non-zero vector $v = a_{1} i + b_{1} j$ ,

$u = \frac{v}{||v||}$

Substitute the values in the above equation,

$u = \frac{5 i + 0 j}{5} u = i$

Therefore, the unit vector in the direction of $v$ is $i$ .

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Find the unit vector in the same direction as $v$ .
role="math" localid="1646752725885" $v = 5 i$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the unit vector.

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Find the unit vector in the same direction as v.role="math" localid="1646752725885" v=5i

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the unit vector.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Applied Mathematics

Probability and Statistics

Decision Maths

Statistics

Study anywhere. Anytime. Across all devices.

Find the unit vector in the same direction as $v$ .
role="math" localid="1646752725885" $v = 5 i$