   Chapter 12.2, Problem 22E

Chapter
Section
Textbook Problem

# Find a + b, 4a + 2b, | a |, and | a − b |22. a = ⟨8, 1, −4⟩, b = ⟨5, −2, 1⟩

To determine

To find: The values of a+b , 4a+2b , |a| , and |ab| .

Explanation

Given:

Vectors a as 8,1,4 and b as 5,2,1 .

Definition:

Consider the two vectors as a=a1,a2,a3 and b=b1,b2,b3 .

Sum of vectors:

The vector sum of two vectors (a+b) is,

a+b=a1,a2,a3+b1,b2,b3=a1+b1,a2+b2,a3+b3

Subtraction of vectors:

The vector subtraction of two vectors (ab) is,

ab=a1,a2,a3b1,b2,b3=a1b1,a2b2,a3b3

Constant multiplication of vector:

The multiplication of vector (ca) is,

ca=ca1,a2,a3=ca1,ca2,ca3

Here,

c is a constant.

Formula:

Consider the expression for magnitude of vector a=a1,a2,a3 (|a|) .

|a|=a12+a22+a32 (1)

Here,

a1 , a2 and a3 are the x, y and z-coordinates of vector respectively.

From definition, write the expression to find sum a+b .

a+b=a1+b1,a2+b2,a3+b3

Substitute 8 for a1 , 5 for b1 , 1 for a2 , –2 for b2 , –4 for a3 , and 1 for b3 ,

a+b=8+5,12,4+1=13,1,3

From definition, write the expression to find 4a+2b

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