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Chapter 10: Q 44. (page 801)

Find a vector in the direction of -1,2,3with magnitude 3.

Short Answer

Expert verified

The required vector is314-1,2,3.

Step by step solution

01

Step 1. Given information.

The given vector is:

v=-1,2,3with magnitude 3.

02

Step 2. Find the norm of the vector.

v=-1,2,3v=-12+22+32=1+4+9=14

Therefore, the norm of the given vector is 14.

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=314-1,2,3


Therefore, the vector in the direction of v=-1,2,3and with a magnitude of 3 is 314-1,2,3.

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Most popular questions from this chapter

What is the definition of the triple scalar product for vectors u, v and w in ℝ3?

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

u×wandw×u

Find u+vandu-valso sketch u,v,u+v,u-v

role="math" localid="1649595165778" u=1,-2andv=-3,6

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(2,−5,1),Q(−4,5,8),R(−1,−5,3)

In Exercises 30–35 compute the indicated quantities when

u=(−3,1,−4),v=(2,0,5),andw=(1,3,13)

u×vandv×u
See all solutions

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