Chapter 9: Q. 29 (page 630)

The vector v is represented by the directed line segment $\underset{P Q}{\to}$ Write v in the form ai + bj and find $∥ v ∥$ .
role="math" localid="1646907960914" $P = (- 1, 2); Q = (3, - 6)$

Short Answer

Expert verified

$v = 2 i - 4 j ∥ v ∥ = 2 \sqrt{5}$

Step by step solution

Step 1. Given information

We have to write the vector v in the form $a i + b j$ and also we have to find $∥ v ∥$ .

Given points are:

$P = (- 1, 2); Q = (3, - 6)$

Step 2. Find the position of vector

To find the position of the vector,

we know that,

$\begin{matrix} v = \vec{P_{1} P_{2}} \end{matrix}$

where,

$P = (x, y)$

it can be written as:

$\begin{matrix} v = <x_{2} - x_{1}, y_{2} - y_{1}> \end{matrix}$

Step 3. Find the vector v

For the points we have,

$\begin{aligned} v = [P, Q] \\ = [(3 - 1), (- 6 - (- 2))] \\ = (2, - 4) \\ = 2 i - 4 j \end{aligned}$

Step 4. Calculate the magnitude

$\begin{aligned} ∥ v ∥ = \sqrt{(2)^{2} + (- 4)^{2}} \\ = \sqrt{4 + 16} \\ = \sqrt{20} \\ = 2 \sqrt{5} \end{aligned}$

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The vector v is represented by the directed line segment $\underset{P Q}{\to}$ Write v in the form ai + bj and find $∥ v ∥$ .
role="math" localid="1646907960914" $P = (- 1, 2); Q = (3, - 6)$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the position of vector

Step 3. Find the vector v

Step 4. Calculate the magnitude

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The vector v is represented by the directed line segment →PQWrite v in the form ai + bj and find ∥v∥.role="math" localid="1646907960914" P=(-1,2);Q=(3,-6)

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the position of vector

Step 3. Find the vector v

Step 4. Calculate the magnitude

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Pure Maths

Applied Mathematics

Logic and Functions

Probability and Statistics

Geometry

Study anywhere. Anytime. Across all devices.

The vector v is represented by the directed line segment $\underset{P Q}{\to}$ Write v in the form ai + bj and find $∥ v ∥$ .
role="math" localid="1646907960914" $P = (- 1, 2); Q = (3, - 6)$