Chapter 3: Q. 20 (page 78)

For the three vectors shown in FIGURE EX3.20, $\vec{A} + \vec{B} + \vec{C} = 1 \hat{j} .$ What is vector $\vec{B} ?$
a. Write $\vec{B}$ in component form.
b. Write $\vec{B}$ as a magnitude and a direction.

Short Answer

Expert verified

(a) $\vec{B} = - 3 \hat{i} + 5 \hat{j} .$

(a) The magnitude of $\vec{B}$ is $\sqrt{37}$ and the direction is $59 . 03^{\circ} .$

Step by step solution

Part (a) Step 1. Given information

The given figure is,

and $\vec{A} + \vec{B} + \vec{C} = 1 \hat{j} .$ We need to determine the vector $\vec{B}$ in component form.

Step 2. Calculation

From the figure,

$\vec{A} = 3 \hat{i}, \vec{C} = - 4 \hat{j} .$

$\vec{A} + \vec{B} + \vec{C} = 1 \hat{j} .$

$3 \hat{i} + \vec{B} - 4 \hat{j} = 1 \hat{j} .$

$\vec{B} = - 3 \hat{i} + 5 \hat{j} .$

Part (b) Step 1. Given information

The given figure is,

and $\vec{A} + \vec{B} + \vec{C} = 1 \hat{j} .$ We need to write $\vec{B}$ as a magnitude and direction.

Step 2. Calculation

From part (a), $\vec{B} = - 3 \hat{i} + 5 \hat{j} .$

role="math" $|\vec{B}| = \sqrt{{(- 3)}^{2} + {(5)}^{2}} .$

$= \sqrt{9 + 25} .$

$= \sqrt{34} .$

$\tan θ = \frac{B_{y}}{B_{x}} .$

$\tan θ = \frac{5}{- 3} .$

$θ = \tan^{- 1} (\frac{5}{- 3}) .$

$= 59 . 03^{\circ} .$

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For the three vectors shown in FIGURE EX3.20, $\vec{A} + \vec{B} + \vec{C} = 1 \hat{j} .$ What is vector $\vec{B} ?$
a. Write $\vec{B}$ in component form.
b. Write $\vec{B}$ as a magnitude and a direction.

Short Answer

Step by step solution

Part (a) Step 1. Given information

Step 2. Calculation

Part (b) Step 1. Given information

Step 2. Calculation

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For the three vectors shown in FIGURE EX3.20, A→+B→+C→=1j^.What is vector B→?a. Write B→in component form. b. Write B→as a magnitude and a direction.

Short Answer

Step by step solution

Part (a) Step 1. Given information

Step 2. Calculation

Part (b) Step 1. Given information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

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For the three vectors shown in FIGURE EX3.20, $\vec{A} + \vec{B} + \vec{C} = 1 \hat{j} .$ What is vector $\vec{B} ?$
a. Write $\vec{B}$ in component form.
b. Write $\vec{B}$ as a magnitude and a direction.