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- 31P. Use the definition of scalar product, a · b = ab cos 0, and the fact that a · b = a,b̟ + a,b, + a̟b, (see Exercise 30) to calculate the angle between the two vectors given by ở 3.0k and b = 2.oî + 1.0ĵ + 3.0k. ssm 3.0î + 3.0j + ilw wwwb) Define a dot product of two vectors A and B, where A = Axi + Avi + Azk and B = Bxi + Byi + BzkRearrange the equation T = 2pi sqrt(L/g) so that is has the form: T2= constant x L
- Evaluate the dot product A · Bif A = 9i +3j and B = 5i – 5j. %3| ? A-B =(b) it (e) It changes with changes in the temperature. (d) it increases if the concentration of one of the reactants is increased. (e) It may be changed by the addition of a catalyst. products is increased. (23) Electric charge, electric potential, energy, temperature etc. are examples of a) Scalar quantity (b) Vector quantity (c) Both (24) An object is thrown straight up. Which of the following is true about the sign of work done by the gravitational force while the object (d) None moves up and then down? A) Work is positive on the way up, work is positive on the way down B) Work is negative on the way up, work is negative on the way down C) Work is negative on the way up, work is positive on the way down D) Work is positive on the way up, work is negative on the way down E) Work is zero the way up, work is zero on the way down (25) What happens to the kinetic energy of a moving object if the net work done is positive? A. The kinetic energy increases C. The kinetic energy remains the…Evaluate the commutator[L,,L, ·L,]. 2, L,]. -L. (a) h’L, (b) 0 (c) h’I, (d) h°L.
- (b) ir; (©) ia. Ans: 0.756 A; 0; 1.244 A, 2a(P) 20 n/nd) For the vectors A=2.00 î - 4.00 ĵ - 3.00 k and B = 5.00 ĵ - 4.00 k find the vector product A X BThe force acting on a particle is given by F(r) = (A/r2)r̂, where A is a positive constant. (a) What are the dimensions of A? Can the force be negative? (b) Sketch F versus r.(c) Find the work done by the force on the particle as it moves from ri = r0 to rf = 5r0. (Use the following as necessary: A, r0.) (d) Check your answer by comparing it with the case of a particle moving under the influence of gravitational force near a planet.