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Chapter 10: Q 49. (page 801)

Find a vector in the direction opposite to 0,-3,4and with magnitude 10.

Short Answer

Expert verified

The required vector is20,3,-4.

Step by step solution

01

Step 1. Given information.

The given vector is:

v=0,-3,4with magnitude 10.

02

Step 2. Find the norm of the vector.

v=0,-3,4v=02+-32+42=0+9+16=25=5

Therefore, the norm of the given vector is 5.

03

Step 3. Find the vector.

We know that the vector in the direction of vis av(-v). Here ais the magnitude of the given vector and the negative sign shows the direction opposite tov=0,-3,4.

The required vector is:

localid="1649520584341" av-v=105-0,-3,4=20,3,-4

Therefore the vector in the direction opposite tov=0,-3,4and with a magnitude of 10 is 20,3,-4.

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Most popular questions from this chapter

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

v=22,12,12

Give an example of three vectors in ℝ3that form a right-handed triple. Explain how you can use the same three vectors to form a left-handed triple.

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

Find the area of the parallelogram determined by the vectors u and v.

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

role="math" localid="1649436488889" (u×v)·wandu·(v×w)

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

v=15,13
See all solutions

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