Chapter 9: Q. 62 (page 603)

Write the vector v in the form ai + bj, given its magnitude $||v||$ and the angle $α$ it makes with the positive x-axis.
$||v|| = 15 α = 315^{o}$

Short Answer

Expert verified

The vector v can be written as $\frac{15 \sqrt{2}}{2} i - \frac{15 \sqrt{2}}{2} j$ .

Step by step solution

Step 1. Given information

We have been given:

$||v|| = 15 α = 315^{o}$

We have to write it in ai+bj form.

Step 2. Substitute the values in v=v(cosαi+sinαj).

$\begin{aligned} v = 15 (\cos (315^{\circ}) i + \sin (315^{\circ}) j) \\ v = 15 \cdot (\frac{\sqrt{2}}{2} i - \frac{\sqrt{2}}{2} j) \\ v = \frac{15 \sqrt{2}}{2} i - \frac{15 \sqrt{2}}{2} j \end{aligned}$

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Write the vector v in the form ai + bj, given its magnitude $||v||$ and the angle $α$ it makes with the positive x-axis.
$||v|| = 15 α = 315^{o}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Substitute the values in v=v(cosαi+sinαj).

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Write the vector v in the form ai + bj, given its magnitude vand the angle αit makes with the positive x-axis. v=15α=315o

Short Answer

Step by step solution

Step 1. Given information

Step 2. Substitute the values in v=v(cosαi+sinαj).

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Applied Mathematics

Geometry

Logic and Functions

Decision Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

Write the vector v in the form ai + bj, given its magnitude $||v||$ and the angle $α$ it makes with the positive x-axis.
$||v|| = 15 α = 315^{o}$