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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

If u and v are nonzero vectors in ℝ3, why do the equations role="math" localid="1649263352081" u·(u×v)=0 and v·(u×v)=0 tell us that the cross product is orthogonal to both u and v?

Sketch the parallelogram determined by the two vectors (1,2)and (3,−1). How can you use the cross product to find the area of this parallelogram?

Find the norm of the vector.v=12,13,14

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

role="math" localid="1649603034674" u=1,-4,6andv=2,-4,7

Calculate the limits in Exercises 25-28, using only the continuity of linear and power functions and the limit rules. Cite each limit rule that you apply.

localid="1648227587052" limx→032x2-4x+1.
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