If the scalar product of two nonzero vectors is zero, what can you conclude about their relative directions?
To explain: the relative directions of the scalar products of two nonzero vectors.
Explanation of Solution
Given information:
The scalar product of a and b is 0
Calculation:
The scalar product of a and b is as follows:
Substitute 0 for
Therefore, the relative directions of the scalar products of two nonzero vectors are perpendicular or orthogonal.
Want to see more full solutions like this?
Chapter 6 Solutions
EBK ESSENTIAL UNIVERSITY PHYSICS, VOLUM
Additional Science Textbook Solutions
College Physics: A Strategic Approach (3rd Edition)
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
Physics for Scientists and Engineers with Modern Physics
University Physics Volume 1
Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)
College Physics (10th Edition)
- The surface of the preceding problem is modified so that the coefficient of kinetic friction is decreased. The same horizontal force is applied to the crate, and after being pushed 8.0 m, its speed is 5.0 m/s. How much work is now done by the force of friction? Assume that the crate starts at rest.arrow_forwardGive an example of a situation in which there is a force and a displacement, but the force does no work. Explain why it does no work.arrow_forwardConsider a particle on which a force acts that depends on the position of the particle. This force is given by . Find the work done by this force when the particle moves from the origin to a point 5 meters to the right on the x-axis.arrow_forward
- Answer the preceding problem using polar coordinates.arrow_forwardGive an example of a situation in which there is a force and a displacement, but the force does no work. Explain why it does no work.arrow_forwardConsider a linear spring, as in Figure 7.7(a), with mass M uniformly distributed along its length. The left end of the spring is fixed, but the right end, at the equilibrium position x=0 , is moving with speed v in the x-direction. What is the total kinetic energy of the spring? (Hint: First express the kinetic energy of an infinitesimal element of the spring dm in terms of the total mass, equilibrium length, speed of the right-hand end, and position along the spring; then integrate.)arrow_forward
- A cart is pulled a distance D on a flat, horizontal surface by a constant farce F that acts at an angle with the horizontal direction. The other forces on the object during this time are gravity (Fw) , normal forces (FN1) and (FN2) , and rolling frictions Fr1 and Fr2 , as shown below What is the work done by each force?arrow_forwardRepeat the preceding problem, but this time, suppose that the work done by air resistance cannot be ignored. Let the work done by the air resistance when the skier goes from A to B along the given hilly path be —2000 J. The work done by air resistance is negative since the air resistance acts in the opposite direction to the displacement. Supposing the mass of the skier is 50 kg, what is the speed of the skier at point B ?arrow_forwardWhat is the dominant factor that affects the speed of an object that started from rest down a frictionless incline if the only work done on the object is from gravitational forces?arrow_forward
- Consider a particle on which several forces act, one of which is known to be constant in time: . As a result, the particle moves along a straight path from a Cartesian coordinate of (0m,0m) to (5m,6m) . What is the work done by ?arrow_forwardAs a young man, Tarzan climbed up a vine to reach his tree house. As he got older, he decided to build and use a staircase instead. Since the work of the gravitational force mg is path Independent, what did the King of the Apes gain in using stairs?arrow_forwardThe force F(x) varies with position, as shown beolow Find the work done by this force on a particle as It moves from x=1.0 m to x=5.0 m.arrow_forward
- University Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice UniversityPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Glencoe Physics: Principles and Problems, Student...PhysicsISBN:9780078807213Author:Paul W. ZitzewitzPublisher:Glencoe/McGraw-HillPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningCollege PhysicsPhysicsISBN:9781938168000Author:Paul Peter Urone, Roger HinrichsPublisher:OpenStax College