Chapter 9: Q. 58 (page 603)

Write the vector v in the form $a i + b j$ , given its magnitude $||v||$ and the angle $α$ it makes with the positive x-axis.
$||v|| = 8, α = 45 °$

Short Answer

Expert verified

The vector in the standard form is $4 \sqrt{2} i + 4 \sqrt{2} j$ .

Step by step solution

Step 1. Given information.

Consider the given question,

$||v|| = 8, α = 45 °$

The vector with magnitude $||v||$ and the angle $α$ is given below,

$v = ||v|| (\cos α i + \sin α j)$

Here, $α$ is the angle between $v, i$ .

Step 2. Write the vector.

The vector with magnitude $8$ and angle $45 °$ is given below,

role="math" localid="1646755598042" $v = ||v|| (\cos α i + \sin α j) v = 8 (\cos 45 ° i + \sin 45 ° j) v = 8 (\frac{1}{\sqrt{2}} i + \frac{1}{\sqrt{2}} j) v = 4 \sqrt{2} i + 4 \sqrt{2} j$

Therefore, the vector with magnitude $8$ and angle $45 °$ is $4 \sqrt{2} i + 4 \sqrt{2} j$ .

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Write the vector v in the form $a i + b j$ , given its magnitude $||v||$ and the angle $α$ it makes with the positive x-axis.
$||v|| = 8, α = 45 °$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Write the vector.

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Write the vector v in the form ai+bj, given its magnitude vand the angle α it makes with the positive x-axis.v=8,α=45°

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Write the vector.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Decision Maths

Logic and Functions

Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

Write the vector v in the form $a i + b j$ , given its magnitude $||v||$ and the angle $α$ it makes with the positive x-axis.
$||v|| = 8, α = 45 °$