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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- 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_forwardIn this problem we are going to consider two different examples of the dot product between two vectors, a force F and a displacement delta r.  (a) if the force vector has a magnitude of F= 19 N, The displacement has a length of deltas=1.2 m, and the angle between the vectors is 35°, what will the dot product between the vector F and the vector delta r be? You can answer in Joules (which is the same as Newton meters) . (B) if the force vector has components fx =8.5 N and F y=12 N,  and the displacement factor has components delta rx=0.15 m and delta ry=0.61m, what is the dot product between them? Again, enter the answer in joules. arrow_forwardSituation 3. For the points O, A, and B: (a) what is the cross product řoa x řOB: (b) determine a unit vector that is perpendicular to roa and foB; and (c) use the cross product to determine the length of the shortest line from point B to the straight line that passes through points O and A. B (4, 4, –4) m FOB "OA А (6, -2, 3) marrow_forward
- Use 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_forwardFor 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_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 dot product A∙ B and its angle of the given vectors: A = 10î - 4ĵ +7 k̂ and B = -2î +ĵ +6 k̂arrow_forward
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