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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

Consider the function f shown in the graph next at the right. Use the graph to make a rough estimate of the average value of f on [−4, 4], and illustrate this average value as a height on the graph.

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(Hint: Think of the xy-plane as part of ℝ3.)
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