   Chapter 11, Problem 19RE

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 = ( 5 , 0 , 0 ) , Q = ( 4 , 4 , 0 ) , R = ( 2 , 0 , 6 )

(a)

To determine

To calculate: For points P=(5,0,0), Q=(4,4,0), and R=(2,0,6). Find thecomponent forms of u and v.

Explanation

Given:

The points are: P=(5,0,0), Q=(4,4,0), and R=(2,0,6). 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. Then,

u1,u2,u3=q1p1,q2p2,q3p3=

(b)

To determine

To calculate: For given P=(5,0,0), Q=(4,4,0), and R=(2,0,6). Find the dot product of u and v.

(c)

To determine

To calculate: For P=(5,0,0), Q=(4,4,0), and R=(2,0,6). Find the value of vv.

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