Chapter 9: Q. 45 (page 603)

Find each quantity if $v = 3 i - 5 j, w = - 2 i + 3 j$ .
$||v|| - ||w||$

Short Answer

Expert verified

The quantity of $||v|| - ||w||$ is $\sqrt{34} - \sqrt{13}$ .

Step by step solution

Step 1. Given information.

Consider the given question,

$v = 3 i - 5 j w = - 2 i + 3 j$

The magnitude of the vector $v = a_{1} i + b_{1} j$ ,

$||v|| = \sqrt{{(a_{1})}^{2} + {(b_{1})}^{2}}$

Compare localid="1646752350191" $v = 3 i - 5 j$ with the standard form localid="1646752360024" $v = a_{1} i + b_{1} j$ ,

$a_{1} = 3, b_{1} = - 5$

Then,

$||v|| = \sqrt{{(3)}^{2} + {(- 5)}^{2}} ||v|| = \sqrt{9 + 25} ||v|| = \sqrt{34}$

Step 2. Compare w with the standard form.

Compare $w = - 2 i + 3 j$ with the standard form $v = a_{1} i + b_{1} j$ ,

$a_{1} = - 2 b_{1} = 3$

Then,

$||w|| = \sqrt{{(- 2)}^{2} + 3^{2}} ||w|| = \sqrt{4 + 9} ||w|| = \sqrt{13}$

Therefore, we can write,

$||v|| - ||w|| = \sqrt{34} - \sqrt{13}$

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Find each quantity if $v = 3 i - 5 j, w = - 2 i + 3 j$ .
$||v|| - ||w||$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Compare w with the standard form.

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Find each quantity if v=3i-5j,w=-2i+3j.v-w

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Compare w with the standard form.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

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Geometry

Study anywhere. Anytime. Across all devices.

Find each quantity if $v = 3 i - 5 j, w = - 2 i + 3 j$ .
$||v|| - ||w||$