Q. 13 Let, A鈫�=4i^-2j^,B鈫�=-3i^+5j聽... [FREE SOLUTION]

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Chapter 3: Q. 13 (page 77)

Let, $\overset{鈫�}{A} = 4 \hat{i} - 2 \hat{j}, \overset{鈫�}{B} = - 3 \hat{i} + 5 \hat{j} a n d \overset{鈫�}{C} = \overset{鈫�}{A} + \overset{鈫�}{B} .$
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 the vector $\overset{鈫�}{C} ?$

Short Answer

Expert verified

(a) $\overset{鈫�}{C} = \hat{i} + 3 \hat{j} .$

(b) The graph is,

Step by step solution

Part (a) Step 1. Given information

It is given that $\overset{鈫�}{A} = 4 \hat{i} - 2 \hat{j}, \overset{鈫�}{B} = - 3 \hat{i} + 5 \hat{j} a n d \overset{鈫�}{C} = \overset{鈫�}{A} + \overset{鈫�}{B} .$ We need to determine the vector $\overset{鈫�}{C}$ in component form.

Step 2. Solution

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

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

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

$= \hat{i} + 3 \hat{j} .$

Part (b) Step 1. Given information

It is given that, $\overset{鈫�}{A} = 4 \hat{i} - 2 \hat{j}, \overset{鈫�}{B} = - 3 \hat{i} + 5 \hat{j} a n d \overset{鈫�}{C} = \overset{鈫�}{A} + \overset{鈫�}{B} .$ From part (b) we need to draw the coordinate system and on it show the vector $\overset{鈫�}{A}, \overset{鈫�}{B}, \overset{鈫�}{C} .$

Step 2. Graph

The graph of $\overset{鈫�}{A} = 4 \hat{i} - 2 \hat{j}, \overset{鈫�}{B} = - 3 \hat{i} + 5 \hat{j} a n d \overset{鈫�}{C} = \hat{i} + 3 \hat{j} .$

Part (c) Step 1. Given information

It is given that $\overset{鈫�}{A} = 4 \hat{i} - 2 \hat{j}, \overset{鈫�}{B} = - 3 \hat{i} + 5 \hat{j} a n d \overset{鈫�}{C} = \overset{鈫�}{A} + \overset{鈫�}{B} .$ From part (a) we need to determine the magnitude and direction of the vector $\overset{鈫�}{C} .$

Step 2. Calculation

$\overset{鈫�}{C} = \hat{i} + 3 \hat{j} .$

$C_{x} = 1, a n d C_{y} = 3 .$

$|C| = \sqrt{C_{x}^{2} + {C_{y}}^{2}} = \sqrt{1^{2} + 3^{2}} = \sqrt{1 + 9} = \sqrt{10} .$

$\tan 胃 = \frac{C_{x}}{C_{y}} .$

$\tan 胃 = \frac{3}{1} .$

$胃 = \tan^{- 1} 3 = 71 . 5^{鈭�} .$

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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

Part (c) Step 1. Given information

Step 2. Calculation

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91影视

Let, A鈫�=4i^-2j^,B鈫�=-3i^+5j^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 the 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

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

Circular Motion and Gravitation

Physics of Motion

Translational Dynamics

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Study anywhere. Anytime. Across all devices.