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Chapter 10: Q 45. (page 801)

Find a vector in the direction of 8,-7,2and with magnitude 2.

Short Answer

Expert verified

The required vector is21178,-7,2.

Step by step solution

01

Step 1. Given information.

The given vector is:

v=8,-7,2with magnitude 2.

02

Step 2. Find the norm of the vector.

v=8,-7,2v=82+-72+22=64+49+4=117

Therefore, the norm of the given vector is 117.

03

Step 3. Find the vector.

We know that the vector in the direction of vis avv. Here ais the magnitude of the given vector.

The required vector is:

avv=21178,-7,2


Therefore the vector in the direction of v=8,-7,2and with a magnitude of 2 is21178,-7,2.

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Most popular questions from this chapter

Find a vector in the direction opposite to-4,5,-1 and with magnitude 3.

If u, v and w are three vectors in ℝ3, which of the following products make sense and which do not?

localid="1649346164463" (a)u·(v·w)(b)u·(v×w)(c)u×(v·w)(d)u×(v×w)

In Exercises 36–41 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(1,6),Q(0,−3),R(−5,4)

(Hint: Think of the xy-plane as part of ℝ3.)

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

v=15,13

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

u×wandw×u
See all solutions

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