Jump to a New ChapterIntroduction to the SAT IIIntroduction to SAT II PhysicsStrategies for Taking SAT II PhysicsVectorsKinematicsDynamicsWork, Energy, and PowerSpecial Problems in MechanicsLinear MomentumRotational MotionCircular Motion and GravitationThermal PhysicsElectric Forces, Fields, and PotentialDC CircuitsMagnetismElectromagnetic InductionWavesOpticsModern PhysicsPhysics GlossaryPractice Tests Are Your Best Friends
 4.1 What’s a Vector? 4.2 Vector Addition 4.3 Vector Subtraction 4.4 Multiplication by a Scalar 4.5 Vector Components

 4.6 Vector Multiplication 4.7 Key Formulas 4.8 Practice Questions 4.9 Explanations
Explanations

1.      A

By adding A to B using the tip-to-tail method, we can see that (A) is the correct answer.

2.      A

The vector 2A has a magnitude of 10 in the leftward direction. Subtracting B, a vector of magnitude 2 in the rightward direction, is the same as adding a vector of magnitude 2 in the leftward direction. The resultant vector, then, has a magnitude of 10 + 2 =12 in the leftward direction.

3.      D

To subtract one vector from another, we can subtract each component individually. Subtracting the x-components of the two vectors, we get 3 –( –1) = 4, and subtracting the y-components of the two vectors, we get 6 – 5 = 1. The resultant vector therefore has an x-component of 4 and a y-component of 1, so that if its tail is at the origin of the xy-axis, its tip would be at (4,1).

4.      D

The dot product of A and B is given by the formula A · B = AB cos . This increases as either A or B increases. However, cos = 0 when = 90°, so this is not a way to maximize the dot product. Rather, to maximize A · B one should set to so cos = 1.

5.      D

Let’s take a look at each answer choice in turn. Using the right-hand rule, we find that is indeed a vector that points into the page. We know that the magnitude of is , where is the angle between the two vectors. Since AB = 12, and since sin , we know that cannot possibly be greater than 12. As a cross product vector, is perpendicular to both A and B. This means that it has no component in the plane of the page. It also means that both A and B are at right angles with the cross product vector, so neither angle is greater than or less than the other. Last, is a vector of the same magnitude as , but it points in the opposite direction. By negating , we get a vector that is identical to .

 Jump to a New ChapterIntroduction to the SAT IIIntroduction to SAT II PhysicsStrategies for Taking SAT II PhysicsVectorsKinematicsDynamicsWork, Energy, and PowerSpecial Problems in MechanicsLinear MomentumRotational MotionCircular Motion and GravitationThermal PhysicsElectric Forces, Fields, and PotentialDC CircuitsMagnetismElectromagnetic InductionWavesOpticsModern PhysicsPhysics GlossaryPractice Tests Are Your Best Friends
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