Chapter 9: Q. 49 (page 603)

find the unit vector in the same direction as $v$ $v = 3 i - 4 j$

Short Answer

Expert verified

The unit vector in the direction of the vector $v = 3 i - 4 j$ is $u = \frac{3}{5} i - \frac{4}{5} j$

Step by step solution

Step 1. Given data

The given vector is

$v = 3 i - 4 j$

Step 2. Finding the magnitude of the given vector

The magnitude of the vector $v = 3 i - 4 j$ is

$|v| = \sqrt{{(3)}^{2} + {(- 4)}^{2}} \Rightarrow |v| = \sqrt{9 + 16} \Rightarrow |v| = \sqrt{25} \Rightarrow |v| = 5$

Step 3. Finding the unit vector

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

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

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

$u = \frac{3 i - 4 j}{|5|} \Rightarrow u = \frac{3}{5} i - \frac{4}{5} j$

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find the unit vector in the same direction as $v$ $v = 3 i - 4 j$

Short Answer

Step by step solution

Step 1. Given data

Step 2. Finding the magnitude of the given vector

Step 3. Finding the unit vector

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find the unit vector in the same direction asvv=3i-4j

Short Answer

Step by step solution

Step 1. Given data

Step 2. Finding the magnitude of the given vector

Step 3. Finding the unit vector

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Geometry

Calculus

Mechanics Maths

Theoretical and Mathematical Physics

Statistics

Study anywhere. Anytime. Across all devices.

find the unit vector in the same direction as $v$ $v = 3 i - 4 j$