   Chapter 11, Problem 20RE

Chapter
Section
Textbook Problem

# Finding Dot ProductsIn Exercises 21 and 22, let u = P Q ⇀ and v = P R ⇀ , and find (a) the component forms of u and v , (b) u ⋅ v , and (c) v ⋅ v . P = ( 2 , − 1 , 3 ) , Q = ( 0 , 5 , 1 ) , R = ( 5 , 5 , 0 )

(a)

To determine

To calculate: For given points P=(2,1,3), Q=(0,5,1), and R=(5,5,0)

Find thecomponent forms of u and v.

Explanation

Given: The points are:

P=(2,1,3), Q=(0,5,1), and R=(5,5,0)

And the vectors are:

u=PQ and v=PR

Formula used: If P(p1,p2,p3) and Q(q1,q2,q3) are the initial and terminal points of a directed line segment, then the component form of the vector u represented by PQ is:

u1,u2,u3=q1p1,q2p2,q3p3

Calculation:

If u=PQ.

u1,u2,u3=q1p1,q2p2,q3p3=02,5(<

(b)

To determine

To calculate: For given P=(2,1,3), Q=(0,5,1), and R=(5,5,0)

The dot product of u and v.

(c)

To determine

To calculate: For given points P=(2,1,3), Q=(0,5,1), and R=(5,5,0). Find the value of vv.

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