Chapter 9: Q. 50 (page 603)

find the unit vector in the same direction as $v$
$v = - 5 i + 12 j$

Short Answer

Expert verified

The unit vector in the direction of the vector $v = - 5 i + 12 j$ is $v = - \frac{5}{13} i + \frac{12}{13} j$ .

Step by step solution

Step 1. Given data

The given vector is

$v = - 5 i + 12 j$

Step 2. Finding the magnitude

The magnitude of the vector $v = - 5 i + 12 j$ is

$|v| = \sqrt{{(- 5)}^{2} + {(12)}^{2}} \Rightarrow |v| = \sqrt{25 + 144} \Rightarrow |v| = \sqrt{169} \Rightarrow |v| = 13$

Step 3. Finding the unit vector

The unit vector $u$ in the direction of is:

Substitute the values of vector and magnitude vector in the formula.

$u = \frac{- 5 i + 12 j}{|13|} \Rightarrow u = \frac{- 5}{13} i + \frac{12}{13} j$

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find the unit vector in the same direction as $v$
$v = - 5 i + 12 j$

Short Answer

Step by step solution

Step 1. Given data

Step 2. Finding the magnitude

Step 3. Finding the unit vector

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find the unit vector in the same direction asvv=-5i+12j

Short Answer

Step by step solution

Step 1. Given data

Step 2. Finding the magnitude

Step 3. Finding the unit vector

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Pure Maths

Theoretical and Mathematical Physics

Discrete Mathematics

Mechanics Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

find the unit vector in the same direction as $v$
$v = - 5 i + 12 j$