   Chapter 12.2, Problem 21E

Chapter
Section
Textbook Problem

# Find a + b, 4a + 2b, | a |, and | a − b |21. a = 4i − 3j + 2k, b = 2i − 4k

To determine

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

Explanation

Given:

Vector a as 4i3j+2k and vector b as 2i4k .

Formula:

Consider the two three-dimensional vectors a as a1i+a2j+a3k and b as b1i+b2j+b3k .

Write the expression for sum of vectors (a+b) .

a+b=a1i+a2j+a3k+b1i+b2j+b3k (1)

Subtraction of vectors:

Write the expression for subtraction of vectors (ab) .

ab=(a1i+a2j+a3k)(b1i+b2j+b3k) (2)

Constant multiplication of vector:

Write the expression for multiplication of vector (ca) .

ca=ca1i+ca2j+ca3k

Here,

c is constant.

Write the expression for magnitude of vector (|a|) .

|a|=a12+a22++a32 (3)

Substitute 4 for a1 , 2 for b1 , –3 for a2 , 0 for b2 , 2 for a3 , and –4 for b3 in equation (1),

a+b=4i3j+2k+2i+0j4k=6i3j2k

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

4a+3b=4(a1i+a2j+a3k)+2(b1i+b2j+b3k)=4a1i+4a2j+4a3k+2b1i+2b2j+2b3k{ ca=ca1i+ca2j+ca3k}

Substitute 4 for

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