   Chapter 12, Problem 2RQ

Chapter
Section
Textbook Problem

# Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.2. For any vectors u and v in V3, |u + v| = |u| + |v|.

To determine

The statement |u+v|=|u|+|v| is true or false.

Explanation

Formula used:

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

Sum of vectors:

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

a+b=a1i+a2j+a3k+b1i+b2j+b3k

a+b=(a1+b1)i+(a2+b2)j+(a3+b3)k (1)

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

|a|=a12+a22+a32 (2)

Consider the given statement.

|u+v|=|u|+|v| (3)

Consider the vectors u as i and v as i.

Find the sum of vectors u and v (u+v) using equation (1)

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