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Chapter 9: Q. 30 (page 630)

The vector v is represented by the directed line segment PQ鈫�. Write v in the form ai + bj and find 鈭�v鈭�.

role="math" localid="1646909539329" P=(0,-2);Q=(-1,1)

Short Answer

Expert verified

v=-1+3j鈭�v鈭�=10

Step by step solution

01

Step 1. Given information

We have to write the vector v in the form ai+bj and also we have to find 鈭�v鈭�.

Given points are:

P=(0,-2);Q=(-1,1)

02

Step 2. Find the position of the vector

To find the position of the vector,

we know that,

v=P1P2鈫�

Where,

P=(x,y)

it can be written as:

v=x2鈭�x1,y2鈭�y1

03

Step 3. Find the vector v

For the points we have,

v=[P,Q]=[(鈭�1鈭�0),(1鈭�(鈭�2))]=(鈭�1,3)=鈭�i+3j

04

Step 4. Calculate the magnitude

鈭�v鈭�=(-1)2+(3)2=1+9=10

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