Chapter 3: Q. 14 (page 77)

Let $\vec{A} = 4 \hat{i} - 2 \hat{j}, \vec{B} = - 3 \hat{i} + 5 \hat{j} a n d \vec{D} = \vec{A} - \vec{B} .$
a. Write vector $\vec{D}$ in component form.
b. Draw a coordinate system and on it show vectors $\vec{A}, \vec{B}, a n d \vec{D} .$
c. What are the magnitude and direction of vector $\vec{D} ?$

Short Answer

Expert verified

(a) $\vec{D} = 7 \hat{i} - 7 \hat{j} .$

(b) The graph is,

Step by step solution

Part (a) Step 1. Given information

It is given that $\vec{A} = 4 \hat{i} - 2 \hat{j}, \vec{B} = - 3 \hat{i} + 5 \hat{j} a n d \vec{D} = \vec{A} - \vec{B} .$

Step 2. Solution

$\vec{A} = 4 \hat{i} - 2 \hat{j}, \vec{B} = - 3 \hat{i} + 5 \hat{j} .$

$\vec{D} = \vec{A} - \vec{B} .$

$= (4 \hat{i} - 2 \hat{j}) - (- 3 \hat{i} + 5 \hat{j}) .$

$= (4 + 3) \hat{i} + (- 2 - 5) \hat{j} .$

$\vec{D} = 7 \hat{i} - 7 \hat{j} .$

Part (b) Step 1. Given information

It is given that $\vec{A} = 4 \hat{i} - 2 \hat{j}, \vec{B} = - 3 \hat{i} + 5 \hat{j} a n d \vec{D} = \vec{A} - \vec{B} = 7 \hat{i} - 7 \hat{j} .$ From, part (a) we need to draw the coordinate system and show the vector $\vec{A}, \vec{B} a n d \vec{D} .$

Step 2. Graph

The graph of $\vec{A} = 4 \hat{i} - 2 \hat{j}, \vec{B} = - 3 \hat{i} + 5 \hat{j} a n d \vec{D} = 7 \hat{i} - 7 \hat{j}$ is

Part (c) Step 1. Given information

It is given that $\vec{A} = 4 \hat{i} - 2 \hat{j}, \vec{B} = - 3 \hat{i} + 5 \hat{j} a n d \vec{D} = \vec{A} - \vec{B} = 7 \hat{i} - 7 \hat{j} .$ We need to determine the magnitude and the direction of the vector $\vec{D} .$

Step 2. Calculation

$\vec{D} = \vec{A} - \vec{B} = 7 \hat{i} - 7 \hat{j} .$ From part (a).

$D_{x} = 7 a n d D_{y} = - 7 .$

$|D| = \sqrt{D_{x}^{2} + D_{y}^{2}} .$

$= \sqrt{{(7)}^{2} + {(- 7)}^{2}} .$

$= \sqrt{49 + 49} = \sqrt{98} = 7 \sqrt{2} .$

$\tan θ = \frac{D_{x}}{D_{y}} = \frac{- 7}{7} = - 1 .$

$θ = \tan^{- 1} (- 1) = - 45^{\circ} .$

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Short Answer

Step by step solution

Part (a) Step 1. Given information

Step 2. Solution

Part (b) Step 1. Given information

Step 2. Graph

Part (c) Step 1. Given information

Step 2. Calculation

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Let A→=4i^-2j^,B→=-3i^+5j^andD→=A→-B→.a. Write vector D→in component form.b. Draw a coordinate system and on it show vectors A→,B→,andD→.c. What are the magnitude and direction of vectorD→?

Short Answer

Step by step solution

Part (a) Step 1. Given information

Step 2. Solution

Part (b) Step 1. Given information

Step 2. Graph

Part (c) Step 1. Given information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

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