   Chapter 12, Problem 5RQ

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.5. For any vectors u and v in V3, u · v = v · u.

To determine

Whether the statement uv=vu is true or false.

Explanation

Formula used:

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

Dot product of vectors:

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

ab=a1,a2,a3b1,b2,b3

ab=a1b1+a2b2+a3b3 (1)

Property 2 of dot product:

Write the expression for property 2 of the dot product of vectors.

ab=ba (2)

Consider the given statement.

uv=vu

From equation (1), it is concluded that the dot product of vectors is always a scalar; not a vector. Hence, it has no direction, only magnitude.

Consider two vectors as u=u1,u2,u3 and v=v1,v2,v3.

Apply the associative law on the dot product of vectors u and v

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