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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91影视

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

Atoms and Radioactivity

Conservation of Energy and Momentum

Work Energy and Power

Space Physics

Translational Dynamics

Electromagnetism

Study anywhere. Anytime. Across all devices.