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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

If u and v are nonzero vectors in 鈩�3, why do the equations role="math" localid="1649263352081" u路(u脳v)=0 and v路(u脳v)=0 tell us that the cross product is orthogonal to both u and v?

In Exercises 22鈥�29 compute the indicated quantities when u=(2,1,鈭�3),v=(4,0,1),andw=(鈭�2,6,5)

localid="1649405204459" role="math" (u脳v)路wandu路(v脳w)

If u and v are vectors in 鈩�3 such that u路v=0 and u脳v=0, what can we conclude about u and v?

If u and v are nonzero vectors in 鈩�3, what is the geometric relationship between u,v and u脳v?

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

u=3,-1,2,v=-4,-6,3
See all solutions

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