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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

For each function f and value x = c in Exercises 35–44, use a sequence of approximations to estimate f'(c). Illustrate your work with an appropriate sequence of graphs of secant lines.

role="math" localid="1648705352169" f(x)=ex,c=0

What is meant by the triangle determined by vectors u and v in ℝ3? How do you find the area of this triangle?

How is the determinant of a 3 × 3 matrix used in the computation of the determinant of two vectorsu=(u1,u2,u3)andv=(v1,v2,v3)?

Find u+vand u-v. Also sketchu,v,u+vand u-v.

role="math" localid="1649578020551" u=3,-4andv=-1,5

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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