Chapter 9: Q. 57 (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.
$||v|| = 5, α = 60 °$

Short Answer

Expert verified

The vector in the standard form is $\frac{5}{2} i + \frac{5 \sqrt{3}}{2} j$ .

Step by step solution

Step 1. Given information.

Consider the given question,

$||v|| = 5, α = 60 °$

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.

The vector with magnitude $5$ and angle $60 °$ is given below,

$v = 5 (\cos 60 ° i + \sin 60 ° j) v = 5 (\frac{1}{2} i + \frac{\sqrt{3}}{2} j) v = \frac{5}{2} i + \frac{5 \sqrt{3}}{2} j$

Therefore, the vector with magnitude $5$ and angle $60 °$ is $\frac{5}{2} i + \frac{5 \sqrt{3}}{2} j$ .

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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.
$||v|| = 5, α = 60 °$

Short Answer

Step by step solution

Step 1. Given information.

Step 2.

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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=5,α=60°

Short Answer

Step by step solution

Step 1. Given information.

Step 2.

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Most popular questions from this chapter

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Logic and Functions

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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.
$||v|| = 5, α = 60 °$