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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

III The bacterium E. coli is a single-cell organism that lives in the BIO gut of healthy animals, including humans. When grown in a uniform medium in the laboratory, these bacteria swim along zig-zag paths at a constant speed of 20μm/s. FIGURE P3.41 shows the trajectory of an E. coli as it moves from point A to point E. What are the magnitude and direction of the bacterium's average velocity for the entire trip?

Are the following statements true or false? Explain your answer.

a. The magnitude of a vector can be different in different coordinate systems.

b. The direction of a vector can be different in different coordinate systems.

c. The components of a vector can be different in different coordinate systems.

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FIGURE P3.25shows vectors A→&B→. Find vector C→such that A→+B→+C→=0→. Write your answer in component form.

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