What are the magnitude and direction of the cross product rAB×F, where rAB is the position vector and F is the force vector, respectively
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What are the magnitude and direction of the cross product rAB×F, where rAB is the position vector and F is the force vector, respectively?
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- 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 27.0Two vectors have the following magnitude, A = 14.1 m and B = 7.9 m. Their vector product is: AxB = -2.9 mi+ 11.1 m k. What is the angle (in degrees) between the vectors A and B? Hint: Use |AxB| = AB sin(0) Note: Bold face letters represents a vector.Using the definition of dot product: A B = ABCOS (0AB) = AxBx + Ay By + A₂B₂ Find the angle between the following vectors: (c) A = 1î + 3j+0k B = 3î + 1) + Ok A = 1î - 3j + 2k B = -31 + 1) + 0k (b) (d) A = 1î + 1ĵ + Ok B = 21-3j+0k A = 21-5j-1k B = 3î + 11 + 3k
- Two vectors have the following magnitude, A = 8.3 m and B = 10.5 m. Their vector product is: A⨯B = -3.7 m i + 7.5 m k.What is the angle (in degrees) between the vectors A and B? Hint: Use |A⨯B| = AB sin(θ)Two vectors are given by a = 1.5î−4.0ĵ and b = −11.9î + 8.1ĵ. What is the magnitude of b? i already found out magnitude of b is 1.44 but how to calculate the angle between vector b and the positive x-axis?A vector and has a magnitude of 7 units, and has a magnitude of 5 units, and the cross product of and has a magnitude of 14 units. Find the angle between and .
- 2. (a) Find the magnitude of the vector −2î + ĵ + 2k̂). (b) Find the magnitude of the vector 3î− 6ĵ + 2k̂). (c) Find the angle between these two vectors. (d) Calculatethe vector sum of the vectors. (e) Calculate the dot product of the vectors. (f) Calculatethe cross product of the vectors.6. Vector A has a magnitude of 5.00 units, and vector B has a magnitude of 9.00 units. The two vectors make an angle of 50.0° with cach other. Find A B. Note: In Problems 7 and 8, calculate numerical answers to three significant figures as usual. 7. Find the scalar product of the vectors in Figure P7.7. 118 32.8 N 132° 17.3 cm Figure P7.7 8. Using the definition of the scalar product, find the angles between (a) A = 3i-2j and B = 4i-4j. (b) A= -2i + 4j and B= 3i- 4j + 2k, and (c) A=i-2j + 2k and B = 3j + 4k. SECTION 7.4 Work Done by a Varying Force 9. A particle is subject to a force F that varies with position as shown in Figure P7.9. Find the work done by the force on the particle as it moves (a) from x = 0 to x = 5.00 m, (b) from x = 5.00 m to x = 10.0 m, and (c) from x= 10.0 m to x = 15.0 m. (d) What is the total work done by the force over the distance x= 0 tox= 15.0 m: 7, (N) X (m) 121 10 12 14 16 Figure P7.9 Problems 9 andl 22.The resultant of two vectors which have equal magnitudes is another vector of magnitude equal to that of the given vectors. What is the angle between the given vectors?
- Two vectors have a dot product of 7 m² and a cross product of magnitude 4.95 m². What is the angle between the two vectors?The vector product of vectors A = 4i + 6j + 8k and B = 6i + 8j – 10k where i, j and k are unit vector1. The vector a has a magnitude of 5.00 units and the vector ba magnitude of 7.00 units. If the angle between the vectors is 53.00, find their scalar product or dot product.