Chapter 9: Q. 35 (page 630)

Find a unit vector in the same direction as $v = - 2 i + j$ .

Short Answer

Expert verified

The unit vector in the direction of $v = - 2 i + j$ is $- \frac{2 \sqrt{5}}{5} i + \frac{\sqrt{5}}{5} j$ .

Step by step solution

Step 1. Given information

We have been given a vector $v = - 2 i + j$ .

We have to find a unit vector in the same direction of v.

Step 2. Write the formula

Unit vector in the direction of $v = a i + b j$ is given as:

$u = \frac{v}{||v||} ||v|| = \sqrt{a^{2} + b^{2}}$

Step 3. Find the unit vector in the direction of v

$u = \frac{v}{∥ v ∥} = \frac{- 2 i + j}{∥ - 2 i + j ∥} = \frac{- 2 i + j}{\sqrt{(- 2)^{2} + 1^{2}}} = \frac{- 2 i + j}{\sqrt{5}} = \frac{- 2}{\sqrt{5}} i + \frac{j}{\sqrt{5}} = \frac{- 2 \sqrt{5}}{5} i + \frac{\sqrt{5}}{5} j$

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Find a unit vector in the same direction as $v = - 2 i + j$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. Write the formula

Step 3. Find the unit vector in the direction of v

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Find a unit vector in the same direction as v=-2i+j.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Write the formula

Step 3. Find the unit vector in the direction of v

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Calculus

Probability and Statistics

Geometry

Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Find a unit vector in the same direction as $v = - 2 i + j$ .