   Chapter 12.1, Problem 17E

Chapter
Section
Textbook Problem

# Think About ItIn Exercises 17 and 18, find r ( t ) ⋅ u ( t ) . Is the result a vector-valued function? Explain. r ( t ) = ( 3 t − 1 ) i + 1 4 t 3 j + 4 k ,     u ( t ) = t 2 i − 8 j + t 3 k

To determine

To calculate: The value of r(t)u(t) when r(t)=(3t1)i+14t3j+4k and

u(t)=t2i+8j+t3k and to explain if the result is a vector-valued function.

Explanation

Given:

The vectors r(t)=(3t1)i+14t3j+4k and u(t)=t2i+8j+t3k.

Formula used:

For any two vectors a=x1i+y1j+z1k and b=x2i+y2j+z2k

ab=x1x2+y1y2+z1z2

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