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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Principles of Physics: A Calculus-Based Text
- 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
- 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_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_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_forward
- Scalars 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_forwardGiven M = î + 5 j - 6 k and N = 2 î - 2 j - 3 k, calculate the vector product M × N. Î + +arrow_forward
- If 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_forwardTwo 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_forward
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