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Chapter 3: Q. 4 (page 77)

Is it possible to add a scalar to a vector? If so, demonstrate. If not, explain why not.

Short Answer

Expert verified

It is not possible to add a vector and scalar quantity together because they have different dimensions.

Step by step solution

01

Step 1. Given information

We need to write is it possible to add a scalar to a vector. If so, we need to demonstrate. If not we need to explain why not.

02

Step 2. Explanation

A vector quantity is defined as a physical quantity that has both magnitude and direction. For example velocity, and displacement. A scalar quantity is a quantity that has only magnitude but no direction. For example distance, and speed. It is impossible to add these two together because of their different dimensions. This basically means that being a vector quantity a particular physical quantity will have both magnitude and direction. Summary of the two quantities together we have to describe the direction of the resultant quantity. As a scalar quantity does not have a direction. It would be next to impossible to describe the direction of the resultant.

For example, let's take a body moving with a velocity of60km/snorth and covering a distance of120km.Now adding these two are impossible as we cannot describe the direction of the resultant quantity.

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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?

Tom is climbing a 3.0−m-long ladder that leans against a vertical wall, contacting the wall 2.5mabove the ground. His weight of680N is a vector pointing vertically downward. (Weight is measured in newtons, abbreviated N.) What are the components of Tom's weight parallel and perpendicular to the ladder?

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.

I You are fixing the root of your house when a hammer breaks loose and slides down. The roof makes an angle of 35°with the horizontal, and the hammer is moving at 4.5m/swhen it reaches the edge. What are the horizontal and vertical components of the hammer's velocity just as it leaves the roof?

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.
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