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Chapter 3: Q. 7 (page 77)

Can a vector have zero magnitudes if one of its components is nonzero? Explain.

Short Answer

Expert verified

It is not possible to have a vector of zero magnitude when one of its components is non-zero.

Step by step solution

01

Step 1. Given information

A vector of zero magnitude is nothing but zero vector. If a vector R→is inclined by an angle θ with respect to x-axis then x-component of is Rcosθ and its y- component isRsinθ .

02

Step 2. Explanation

If vector R→ is a zero vector, then its magnitude R = 0 . It means that both of its components Rcosθ andRsinθ terms should be equal to zero.

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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.

While vacationing in the mountains you do some hiking. In the morning, your displacement is S→morning=(2000m, east )+(3000m, north )+(200m, vertical \()\). After lunch, your displacement is S→afternoon=(1500m, west )+(2000m, north )−(300m, vertical).

a. At the end of the hike, how much higher or lower are you compared to your starting point?

b. What is the magnitude of your net displacement for the day?

Let B→=5.0m,30∘counterclockwisefromvertical.Find the xandy-components of localid="1651138630094" B→in each of the two coordinate systems shown in FIGURE EX3.18.

Suppose two vectors have unequal magnitudes. Can their sum be zero? Explain.

I A pine cone falls straight down from a pine tree growing on a20° slope. The pine cone hits the ground with a speed of 10m/s. What is the component of the pine cone's impact velocity (a) parallel to the ground and (b) perpendicular to the ground?
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