Q9P Two vectors are given by,聽a鈬赌=... [FREE SOLUTION]

Chapter 3: Q9P (page 57)

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

Short Answer

Expert verified

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

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

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

Given

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

To finda⇀+b⇀

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

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

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

To finda⇀-b⇀

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

Thus

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

To findc⇀

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

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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⇀

One App. One Place for Learning.

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91影视

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

Thermodynamics

Linear Momentum

Classical Mechanics

Geometrical and Physical Optics

Physical Quantities And Units

Atoms and Radioactivity

Study anywhere. Anytime. Across all devices.