Q. 12 Let, A鈫�=2i^+3j^,B鈫�=2i^-4j^聽... [FREE SOLUTION]

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Chapter 3: Q. 12 (page 77)

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

Short Answer

Expert verified

(a) $\overset{鈫�}{C} = 4 \hat{i} - \hat{j} .$

(b) The graph is,

Step by step solution

Part (a) Step 1. Given information

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

Step 2. Solution

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

role="math" $\overset{鈫�}{C} = \overset{鈫�}{A} + \overset{鈫�}{B} .$

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, $\overset{鈫�}{A} = 2 \hat{i} + 3 \hat{j}, \overset{鈫�}{B} = 2 \hat{i} - 4 \hat{j} a n d \overset{鈫�}{C} = \overset{鈫�}{A} + \overset{鈫�}{B} .$ We need to draw the coordinate system.

Step 2. Graph of the A→,B→ and C→

The graph of $\overset{鈫�}{A}, \overset{鈫�}{B} a n d \overset{鈫�}{C}$ is,

Part (c) Step 1. Given information

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

Step 2. Calculation

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

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 $\tan 胃 = \frac{C_{y}}{C_{x}} .$

$胃 = \tan^{- 1} (\frac{- 1}{4}) = 14^{鈭�} .$

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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 of the A→,B→ and C→

Part (c) Step 1. Given information

Step 2. Calculation

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

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

Recommended explanations on Physics Textbooks

Dynamics

Electrostatics

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Modern Physics

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