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Chapter 3: Q. 6 (page 77)

Can a vector have a component equal to zero and still have nonzero magnitude? Explain.

Short Answer

Expert verified

Yes, a vector can have a given component along a line and still can have non-zero magnitude.

Step by step solution

01

Step 1. Given information

We need to write can a vector have a component equal to zero and still have a non-zero magnitude. We need to explain it.

02

Step 2. Explanation

Thus, A→x=0,andA→y=A→.

A→=Ax2+Ay2.

=Ay2.

Ay.

Thus, a vector can have a given component along a line and still can have non-zero magnitude.

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Most popular questions from this chapter

I A runner is training for an upcoming marathon by running around a 100-m-diameter circular track at constant speed. Let a coordinate system have its origin at the center of the circle with the -axis pointing east and the -axis north. The runner starts at and runs \(2.5\) times around the track in a clockwise direction. What is his displacement vector? Give your answer as a magnitude and 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 A→=4i^-2j^,B→=-3i^+5j^andF→=A→-4B→.

a. Write vector F→in component form.

b. Draw a coordinate system and on it show vectors A→,B→andF→.

c. What are the magnitude and direction of vectorF→?

| The treasure map in FIGURE P3.40 gives the following directions to the buried treasure: "Start at the old oak tree, walk due north for 500 paces, then due east for 100 paces. Dig." But when you arrive, you find an angry dragon just north of the tree. To avoid the dragon, you set off along the yellow brick road at an angle east of north. After walking 300 paces you see an opening through the woods. Which direction should you go, and how far, to reach the treasure?

a. What is the angle ϕbetween vectors E→andF→in FIGURE P3.24?

b. Use geometry and trigonometry to determine the magnitude and direction of G→=E→+F→.

c. Use components to determine the magnitude and direction of G→=E→+F→.
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