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Chapter 3: Q. 3 (page 77)

If C→=A→+B→,Can C=0?Can C<0?For each, show how or explain why not.

Short Answer

Expert verified

The magnitude of vectorCcan be 0but it magnitudeCcanot be less than 0.

Step by step solution

01

Step 1. Given information

It is given that C→=A→+B→.We need to write can C=0and can C<0.For each we need to showhow or explain why not.

02

Step 2. Explanation

Length of a vector,

A vector either has length, or it has not. Its magnitude cannot be negative.

Ccan be 0if A→=-B→,in which case the sumC→is a vector of length0.

03

Step 3. Explanation

The magnitude of a vector is always positive so the magnitude of vector C→can't be negative.

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Most popular questions from this chapter

II A flock of ducks is trying to migrate south for the winter, but they keep being blown off course by a wind blowing from the west at 6.0m/s. A wise elder duck finally realizes that the solution is to fly at an angle to the wind. If the ducks can fly at 8.0m/srelative to the air, what direction should they head in order to move directly south?

How would you define the zero vector0→?

For the three vectors shown in FIGURE EX3.20, A→+B→+C→=1j^.What is vector B→?

a. Write B→in component form.

b. Write B→as a magnitude and a direction.

II Draw each of the following vectors, label an angle that specifies the vector's direction, and then find the vector's magnitude and direction.

a.A→=3i^+7j^

b.a=(−2i^+4.5j^)m/s2

c.v→=(14i^−11j^)m/s

d.r→=(−2.2i^−3.3j^)m

Let E→=2i^+3j^andF→=2i^-2j^.Find the magnitudes of

a.E→andF→b.E→+F→c.-E→-2F→
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