Q. 16 Let A鈫�=4i^-2j^,B鈫�=-3i^+5j^聽... [FREE SOLUTION]

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Chapter 3: Q. 16 (page 78)

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

Short Answer

Expert verified

(a) $\overset{鈫�}{F} = 20 \hat{i} - 22 \hat{j} .$

(b) The graph is,

Step by step solution

Part (a) Step 1. Given information

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

Step 2. Solution

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

$\overset{鈫�}{F} = \overset{鈫�}{A} - 4 \overset{鈫�}{B} .$

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

$= 4 \hat{i} - 2 \hat{j} + 12 \hat{i} - 20 \hat{j} .$

$= 20 \hat{i} - 22 \hat{j} .$

Part (b) Step 1. Given information

It is given that $\overset{鈫�}{A} = 4 \hat{i} - 2 \hat{j}, \overset{鈫�}{B} = - 3 \hat{i} + 5 \hat{j} a n d \overset{鈫�}{F} = \overset{鈫�}{A} - 4 \overset{鈫�}{B} = 20 \hat{i} - 22 \hat{j} .$ We need to draw the coordinate system and on it show vector $\overset{鈫�}{A}, \overset{鈫�}{B} a n d \overset{鈫�}{F} .$

Step 2. Graph

The graph of $\overset{鈫�}{A} = 4 \hat{i} - 2 \hat{j}, \overset{鈫�}{B} = - 3 \hat{i} + 5 \hat{j} a n d \overset{鈫�}{F} = 20 \hat{i} - 22 \hat{j}$ is,

Part (c) Step 1. Given information

It is given that $\overset{鈫�}{A} = 4 \hat{i} - 2 \hat{j}, \overset{鈫�}{B} = - 3 \hat{i} + 5 \hat{j} a n d \overset{鈫�}{F} = \overset{鈫�}{A} - 4 \overset{鈫�}{B} = 20 \hat{i} - 22 \hat{j} .$ We need to determine the magnitude and direction of $\overset{鈫�}{F} .$

Step 2. Calculation

$\overset{鈫�}{F} = 20 \hat{i} - 22 \hat{j} .$

$F_{x} = 20 a n d F_{y} = - 22 .$

$|\overset{鈫�}{F}| = \sqrt{{(F_{x})}^{2} + {(F_{y})}^{2}} .$

$= \sqrt{{(20)}^{2} + {(- 22)}^{2} .}$

$= \sqrt{400 + 484} .$

$= \sqrt{884} .$

$= 2 \sqrt{221} .$

$\tan 胃 = \frac{F_{y}}{F_{x}} = \frac{- 22}{20} = - \frac{11}{10} .$

$胃 = \tan^{- 1} (\frac{- 11}{10}) .$

$= - 47 . 7^{鈭�} .$

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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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Let A鈫�=4i^-2j^,B鈫�=-3i^+5j^andF鈫�=A鈫�-4B鈫�.a. Write vector F鈫�in component form.b. Draw a coordinate system and on it show vectors A鈫�,B鈫�andF鈫�.c. What are the magnitude and direction of vectorF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

Force

Further Mechanics and Thermal Physics

Thermodynamics

Astrophysics

Circular Motion and Gravitation

Electricity and Magnetism

Study anywhere. Anytime. Across all devices.