Chapter 3: Q9P (page 57)

Two vectors are given by, $\overset{⇀}{a} = (4.0 m) \hat{i} - (3.0 m) \hat{j} + (1.0 m) \hat{k}$ And $\overset{⇀}{b} = (- 1.0 m) \hat{i} + (1.0 m) \hat{j} + (4.0 m) \hat{k}$ In unit-vector notation, findrole="math" localid="1656159321000" $(a) \overset{⇀}{a} + \overset{⇀}{b}, (b) \overset{⇀}{a} - \overset{⇀}{b}$ and a third vector $\overset{⇀}{c}$ such that $\overset{⇀}{a} - \overset{⇀}{b} = 0$

Short Answer

Expert verified

$a) \overset{⇀}{a} + \overset{⇀}{b}, = (3) \overset{⇀}{i} - (2) \overset{⇀}{j} + (5) \overset{⇀}{k} b) \overset{⇀}{a} + \overset{⇀}{b}, = (5) \overset{⇀}{i} - (4) \overset{⇀}{j} + (3) \overset{⇀}{k} c) \overset{⇀}{c} = (- 5) \overset{⇀}{i} + (4) \overset{⇀}{j} + (3) \overset{⇀}{k}$

Step by step solution

To understand the concept of vector addition and subtraction

Components of all the vectors which are associated with the same unit can be added or subtracted. The addition and subtraction of the vectors can be written as

$\overset{⇀}{a} + \overset{⇀}{b} = (A_{x} + B_{x}) \overset{⇀}{I} + (A_{y} + B_{y}) \overset{⇀}{j} + (A_{z} + B_{z}) \overset{⇀}{k} \overset{⇀}{a} + \overset{⇀}{b} = (A_{x} - B_{x}) \overset{⇀}{I} + (A_{y} - B_{y}) \overset{⇀}{j} + (A_{z} - B_{z}) \overset{⇀}{k}$

Given

$\overset{⇀}{a} = (4) \overset{⇀}{i} - (3) \overset{⇀}{j} + (1) \overset{⇀}{k} \overset{⇀}{b} = (- 1) \overset{⇀}{i} - (1) \overset{⇀}{j} + (4) \overset{⇀}{k}$

To finda⇀+b⇀

$\overset{⇀}{a} + \overset{⇀}{b} = [(4) \overset{⇀}{i} - (3) \overset{⇀}{j} + (1) \overset{⇀}{k}] + [(- 1) \overset{⇀}{i} - (1) \overset{⇀}{j} + (4) \overset{⇀}{k}]$

According to vector algebra, we can add or subtract vectors in same direction. Thus,

$\overset{⇀}{a} + \overset{⇀}{b} = (3) \overset{⇀}{i} - (2) \overset{⇀}{j} + (5) \overset{⇀}{k}$

To finda⇀-b⇀

$\overset{⇀}{a} - \overset{⇀}{b} = [(4) \overset{⇀}{i} - (3) \overset{⇀}{j} + (1) \overset{⇀}{k}] + [(- 1) \overset{⇀}{i} - (1) \overset{⇀}{j} + (4) \overset{⇀}{k}]$

Thus

$\overset{⇀}{a} - \overset{⇀}{b} = (5) \overset{⇀}{i} - (4) \overset{⇀}{j} + (3) \overset{⇀}{k}$

To findc⇀

$\overset{⇀}{a} - \overset{⇀}{b} + \overset{⇀}{c} = 0 \overset{⇀}{c} = \overset{⇀}{b} - \overset{⇀}{a} \overset{⇀}{c} = (- 1) \overset{⇀}{i} - (1) \overset{⇀}{j} + (4) \overset{⇀}{k} - ((- 4) \overset{⇀}{i} - (3) \overset{⇀}{j} + (1) \overset{⇀}{k}) \overset{⇀}{c} = (- 5) \overset{⇀}{i} + (4) \overset{⇀}{j} + (3) \overset{⇀}{k}$

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Short Answer

Step by step solution

To understand the concept of vector addition and subtraction

To finda⇀+b⇀

To finda⇀-b⇀

To findc⇀

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Two vectors are given by,a⇀=(4.0m)i^-(3.0m)j^+(1.0m)k^Andb⇀=(-1.0m)i^+(1.0m)j^+(4.0m)k^In unit-vector notation, findrole="math" localid="1656159321000" (a)a⇀+b⇀,(b)a⇀-b⇀and a third vectorc⇀such thata⇀-b⇀=0

Short Answer

Step by step solution

To understand the concept of vector addition and subtraction

To finda⇀+b⇀

To finda⇀-b⇀

To findc⇀

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Linear Momentum

Fields in Physics

Physical Quantities And Units

Nuclear Physics

Physics of Motion

Circular Motion and Gravitation

Study anywhere. Anytime. Across all devices.