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)
Want to see the full answer?
Check out a sample textbook solutionChapter 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
- For 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_forwardFind the vector product (a X b) of the two given vectors: a = 2i + 3j + 4k, b = 3i + 5j. Here, i, j & k are unit vectors along three mutually perpendicular axes. a) -20i + 12j + k b) 10i + 6j + 1/2k c) 20i – 12j – k d) 10i – 6j -1/2karrow_forward
- Use the definition of scalar product, ?→⋅?→�→⋅�→ = ab cos θ, and the fact that ?→⋅?→�→⋅�→ = axbx + ayby + azbz to calculate the angle between the two vectors given by ?→=6.0?̂ +6.0?̂+6.0?̂�→=6.0�̂+6.0�̂+6.0�̂ and ?→=2.0?̂ +2.0?̂+3.0?̂�→=2.0�̂+2.0�̂+3.0�̂.arrow_forwardIf you had two vectors a = 2z(hat) and b = x(hat) + 2y(hat) + 3z(hat). What would the addition of the two vectors look like physically? Subtraction? dot product? Cross product? Can you draw the vectors out in each instance.arrow_forwardGiven two vectors A⃗ = 4.20 i^+ 7.60 j^ and B⃗ = 5.70 i^− 2.40 j^ , find the scalar product of the two vectors A⃗ and B⃗ . Find the angle between these two vectors.arrow_forward
- Two vectors in Cartesian coordinates have components A=(2,3,2) and B=(4,-1,7). What is the dot product of vector A with vector B? A•B=arrow_forwardGiven two vectors Á = 4î + 3j and B = 12î – 5j a)Find the scalar product A · B. b)Find the angle between the two vectors. c)Find the vector product A × B.arrow_forwardThe vector product of vectors A → and B → has magnitude 12.0 m2m2 and is in the +z+-direction. Vector A → has magnitude 4.0 mm and is in the −x− -direction. Vector B → has no x-component. What is the directional angle θ of vector B → in the xy-plane measured counterclockwise from the +x+ -direction?arrow_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