Chapter 9: Q. 17 (page 632)

In Problems 14–18, $P_{1} = (3 \sqrt{2}, 7 \sqrt{2})$ and $P_{2} = (8 \sqrt{2}, 2 \sqrt{2})$ .
Find the direction angle of $v$ .

Short Answer

Expert verified

The directional angles are $α = 45 ° β = 315 °$

Step by step solution

Step 1. Given information

The points are

$P_{1} = (3 \sqrt{2}, 7 \sqrt{2}) P_{2} = (8 \sqrt{2}, 2 \sqrt{2})$

Step 2. Find the direction angle of v.

Position vector $v$ is equal to $\vec{P_{1} P_{2}}$

$\vec{P_{1} P_{2}} = \vec{O P_{2}} - \vec{O P_{1}} = (8 \sqrt{2} \hat{i} + 2 \sqrt{2} \hat{j}) - (3 \sqrt{2} \hat{i} + 7 \sqrt{2} \hat{j}) = 5 \sqrt{2} \hat{i} - 5 \sqrt{2} \hat{j}$

The direction angles $α, β$ of $v = a \hat{i} + b \hat{j}$ are given by

localid="1647012506438" $\cos α = \frac{a}{\sqrt{a^{2} + b^{2}}} = \frac{5 \sqrt{2}}{\sqrt{{(5 \sqrt{2})}^{2} + {(- 5 \sqrt{2})}^{2}}} = \frac{1}{\sqrt{2}} α = 45 ° \cos β = \frac{b}{\sqrt{a^{2} + b^{2}}} = \frac{- 5 \sqrt{2}}{\sqrt{{(5 \sqrt{2})}^{2} + {(- 5 \sqrt{2})}^{2}}} = - \frac{1}{\sqrt{2}} β = 315 °$

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In Problems 14–18, $P_{1} = (3 \sqrt{2}, 7 \sqrt{2})$ and $P_{2} = (8 \sqrt{2}, 2 \sqrt{2})$ .
Find the direction angle of $v$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the direction angle of v.

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In Problems 14–18, P1=32,72and P2=82,22.Find the direction angle of v.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the direction angle of v.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Geometry

Applied Mathematics

Mechanics Maths

Decision Maths

Calculus

Study anywhere. Anytime. Across all devices.

In Problems 14–18, $P_{1} = (3 \sqrt{2}, 7 \sqrt{2})$ and $P_{2} = (8 \sqrt{2}, 2 \sqrt{2})$ .
Find the direction angle of $v$ .