Physics for Scientists and Engineers, 6e

Chapter 3 - Vectors

Which of the following are vector quantities?

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1. your age, speed, mass

2. acceleration, velocity

Scalars: your age, speed, mass. None of these quantities has a direction. Vectors: acceleration, velocity. For these quantities, the direction is necessary to specify the quantity completely.

The magnitudes of two vectors A and B are A = 12 units and B = 8 units. Which of the following pairs of numbers represents the largest and smallest possible values for the magnitude of the resultant vector R = A + B?

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1. 14.4 units, 4 units

2. 12 units, 8 units

3. 20 units, 4 units

4. none of these answers

The resultant has its maximum magnitude A + B = 12 + 8 = 20 units when vector A is oriented in the same direction as vector B. The resultant vector has its minimum magnitude A – B = 12 – 8 = 4 units when vector A is oriented in the direction opposite vector B.

If vector B is added to vector A, under what condition does the resultant vector A + B have magnitude A + B?

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1. A and B are parallel and in the same direction.

2. A and B are parallel and in opposite directions.

3. A and B are perpendicular.

The magnitudes will add numerically only if the vectors are in the same direction.

Choose the correct response to make the sentence true: A component of a vector is _____ larger than the magnitude of the vector.

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1. always

2. never

3. sometimes

From the Pythagorean theorem, the magnitude of a vector is always larger than the absolute value of each component, unless there is only one nonzero component, in which case the magnitude of the vector is equal to the absolute value of that component.

If at least one component of a vector is a positive number, the vector cannot

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1. have any component that is negative

2. be zero

3. have three dimensions

From the Pythagorean theorem, we see that the magnitude of a vector is nonzero if at least one component is nonzero.

If A + B = 0, the corresponding components of the two vectors A and B must be

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1. equal

2. positive

3. negative

4. of opposite sign

Each set of components, for example, the two x components Ax and Bx, must add to zero, so the components must be of opposite sign.