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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, ${\vec{A}}_{x} = 0, a n d {\vec{A}}_{y} = |\vec{A}| .$

$[\vec{A}] = \sqrt{A_{x}^{2} + A_{y}^{2}} .$

$= \sqrt{A_{y}^{2}} .$

$A_{y} .$

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

Kami is walking through the airport with her two-wheeled

suitcase. The suitcase handle is tilted 40° from vertical, and

Kami pulls parallel to the handle with a force of 120 N. (Force is

measured in newtons, abbreviated N.) What are the horizontal and

vertical components of her applied force?

I A cannon tilted upward at $30^{°}$ fires a cannonball with a speed of $100 m / s$ . What is the component of the cannonball's velocity parallel to the ground?

FIGURE $P 3.26$ shows vectors $\vec{A} & \vec{B}$ . Find $\vec{D} = 2 \vec{A} + \vec{B}$ . Write your answer in component form.

6. I Draw each of the following vectors. Then find its - and components.

a. $\vec{a} = (3.5 m / s^{2}$ , negative x-direction)

b. $\vec{v} = (440 m / s, 30^{°}$ below the positive x-axis )

c. $\vec{r} = (12 m, 40^{°}$ above the positive x-axis )

Let $\vec{E} = 2 \hat{i} + 3 \hat{j} a n d \vec{F} = 2 \hat{i} - 2 \hat{j} .$ Find the magnitudes of

a. $\vec{E} a n d \vec{F}$ b. $\vec{E} + \vec{F}$ c. $- \vec{E} - 2 \vec{F}$

See all solutions

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