Chapter 3: Q. 12 (page 77)

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

Short Answer

Expert verified

(a) $\vec{C} = 4 \hat{i} - \hat{j} .$

(b) The graph is,

Step by step solution

Part (a) Step 1. Given information

It is given that $\vec{A} = 2 \hat{i} + 3 \hat{j}, \vec{B} = 2 \hat{i} - 4 \hat{j} a n d \vec{C} = \vec{A} + \vec{B} .$ We need to determine the vector $\vec{C}$ in component form.

Step 2. Solution

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

role="math" $\vec{C} = \vec{A} + \vec{B} .$

role="math" localid="1649230879168" $= 2 \hat{i} + 3 \hat{j} + 2 \hat{i} - 4 \hat{j} .$

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

$= 4 \hat{i} - \hat{j} .$

Part (b) Step 1. Given information

It is given that, $\vec{A} = 2 \hat{i} + 3 \hat{j}, \vec{B} = 2 \hat{i} - 4 \hat{j} a n d \vec{C} = \vec{A} + \vec{B} .$ We need to draw the coordinate system.

Step 2. Graph of the A→,B→ and C→

The graph of $\vec{A}, \vec{B} a n d \vec{C}$ is,

Part (c) Step 1. Given information

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

Step 2. Calculation

From part (a) $\vec{C} = 4 \hat{i} - \hat{j} .$

Thus, $C_{x} = 4, C_{y} = - 1 .$

$|C| = \sqrt{C_{x}^{2} + C_{y}^{2}} .$

$= \sqrt{{(4)}^{2} + {(- 1)}^{2}} .$

$= \sqrt{16 + 1} .$

$= \sqrt{17},$

and $\tan θ = \frac{C_{y}}{C_{x}} .$

$θ = \tan^{- 1} (\frac{- 1}{4}) = 14^{\circ} .$

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

Short Answer

Step by step solution

Part (a) Step 1. Given information

Step 2. Solution

Part (b) Step 1. Given information

Step 2. Graph of the A→,B→ and C→

Part (c) Step 1. Given information

Step 2. Calculation

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

Short Answer

Step by step solution

Part (a) Step 1. Given information

Step 2. Solution

Part (b) Step 1. Given information

Step 2. Graph of the A→,B→ and C→

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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