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Which of the following statements is true about the relationship between the dot product of two vectors and the product of the magnitudes of the vectors? (a)
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Chapter 7 Solutions
Physics for Scientists and Engineers with Modern Physics
- Show that when A+B=C then A2+B2+2ABcos , where is the angle between vectors A and B .arrow_forwardFind the angle between vectors for (a) D=(-3.0i-4.0j)m and A=(-3.0i+4.0j)m and (b) D=(2.0i+4.0j+K)m and B=(-2.0i+3.0j+2.0K)m .arrow_forwardIf the dot product of two vectors vanishes, what can you say about their directions?arrow_forward
- When is the magnitude of the vector product of two vectors the largest? When the two vectors are perpendicular. Only if the two vectors are anti-parallel (180°). No answer text provided. When the two vectors are either parallel (O°) or anti-parallel (180°). Only if the two vectors are parallel (0°). When the angle between the two vectors is 45°.arrow_forwardUse the definition of scalar product, a = ab cos 0, and the fact that a . the two vectors given by a = 3.01 +3.0 + 3.0k and b Number i Units = axbx + ab + a₂b₂ to calculate the angle between 4.0î + 9.0ĵ + 7.0k. =arrow_forwardProblem 4: It should be obvious that the magnitude of a vector is independent of the choice of coordinate system. This implies that r r is the same for any set of axes. Use this to prove that the dot product of two different vectors r.s is also independent of coordinate system. [Hint: Consider the length of r + s.]arrow_forward
- For the pair of vectors A = (6.00î + 4.00ĵ) and B = (9.0oî – 6.00ĵ) in the xy plane, determine the following. (Enter all angle answers between 0 and 180°.) %3D (a) The scalar product A: B = (b) The angle 0 between the vectors (c) The angles a and ß which are respectively the (smallest) angles between the vector A and the positive x and positive y axes a = %D (d) The angles y and 8, which are respectively the (smallest) angles between the vector B and the positive x and positive y axes Y 8 %3Darrow_forwardFor the pair of vectors A = (6.00î + 4.00j) and B = (9.00î – 6.00j) in the xy plane, determine the following. (Enter all angle answers between 0 and 180°.) (a) The scalar product A·B = (b) The angle 0 between the vectors (c) The angles a and B which are respectively the (smallest) angles between the vector A and the positive x and positive y axes a = B = (d) The angles y and 8, which are respectively the (smallest) angles between the vector B and the positive x and positive y axes 8 =arrow_forwardScalars and vectors: Vector A has a magnitude of 9.0 and Vector B has a magnitude of 3.0. If the vectors are at an angle of 30.0º, what is the magnitude of the cross product A x B? Here are the choices: 13.5 16.2 23.4 27.0arrow_forward
- 2. (a) Find the angle between the two vectors A= 2î + 4j – 4k andB= –2î + 2j – k. (b) Find C= AX B (Remember that this is vector product.)arrow_forwardIn this problem we are going to consider two different examples of the dot product between two vectors, a force F and a displacement Δr. If the force vector has a magnitude of F = 14.5 N, the displacement has a length of Δr = 0.75 m, and the angle between the vectors is 45°, what will the dot product between the vector F and the vector Δr be? You can answer in joules (which is the same as newton-meters). If the force vector has components Fx = 7.5 N and Fy = 13.8 N, and the displacement vector has components Δrx = 0.25 m and Δry = 0.63 m, what is the dot product between them? Again, enter your answer in joules.arrow_forwardUsing the definition of dot product: Ax B= (A,B₂ - A₂By)i + (A₂Bx − AxB₂)j + (AxBy - Ay Bx)k Find the cross product Ax B the following vectors: (a) U A = 11 + 3) + 0k B = 3î + 1ĵ + 0k A = 11 - 3j+2k B = -31 + 1ĵ+ 0k (b) (d) A = 1î + 1ĵ + Ok B = 2î - 3j+0k A = 21-5j-1k B = 3î + 1ĵ+ 3karrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningUniversity Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice University
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