   Chapter 12, Problem 1RQ

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.1. If u = ⟨u1, u2⟩ and v = ⟨v1, v2⟩, then u · v = ⟨u1v1, u2v2⟩.

To determine

The statement uv=u1v1,u2v2 is true or false.

Explanation

Formula used:

Consider two two-dimensional vectors as a=a1,a2 and b=b1,b2.

Write the expression for the dot product of vectors a and b.

ab=a1,a2b1,b2

ab=a1b1+a2b2 (1)

Consider the given statement.

uv=u1v1,u2v2

Find the dot product of vectors u and v using equation (1)

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