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Chapter 10: Q 21. (page 812)

In Exercises 20-23, find the dot product of the given pairs of vectors and the angle between the two vectors.

u=2,0,-5,v=-3,7,-1

Short Answer

Expert verified

The dot product is-1 and the angle isrole="math" localid="1649664356753" cos-1-11711.

Step by step solution

01

Step 1. Given information.

The given pairs of vectors are:

u=2,0,-5andv=-3,7,-1

02

Step 2. Find the dot product.

The dot product is: u路v=u1v1+u2v2+u3v3

u=2,0,-5andv=-3,7,-1=2-3+07+-5-1=-6+0+5=-1

Therefore, the dot product of the given two vectors u=2,0,-5andv=-3,7,-1is-1.

03

Step 3. Find the angle between the two vectors.

The formula for the angle between the two vectors is:

cos胃=u路vuv

u=2,0,-5andv=-3,7,-1u路v=-1u=22+02+-524+0+25=29v=-32+72+-129+49+1=59

Then,

role="math" localid="1649664305708" cos胃=u路vuvcos胃=-12959胃=cos-1-11711

Therefore, the angle isrole="math" localid="1649664318896" cos-1-11711.

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Most popular questions from this chapter

In Exercises 36鈥�41 use the given sets of points to find:

(a) A nonzero vector N perpendicular to the plane determined by the points.

(b) Two unit vectors perpendicular to the plane determined by the points.

(c) The area of the triangle determined by the points.

P(3,1,8),Q(0,6,鈭�1),R(鈭�3,5,鈭�3)

In Exercises 30鈥�35 compute the indicated quantities when u=(鈭�3,1,鈭�4),v=(2,0,5),andw=(1,3,13)

role="math" localid="1649434688557" v脳wandw脳v

Find PQ鈫�

P=1,-2,5,Q=1,-7,-2

Give an example of three vectors in 鈩�3that form a right-handed triple. Explain how you can use the same three vectors to form a left-handed triple.

In Exercises 37鈥�42, find v and find the unit vector in the direction of v.

v=13,-23
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