Please answer sub c only a) Let the 3-D vector a make angles a, ß and y with the coordinate axes. Show thatâ = cos ai + cos Bj + cos yk is a unit vector in the direction of the vector a. Show alsothat cos²a + cos?B + cos²y = 1.b) The path of a particle is given by the position vector 7(t) = a sin ti + a cos tj + b tk, where aand b are real constants.i) Sketch the graph of the curve traced by the particle as t varies.ii) Find the length of the curve between the points correspondong to t = 0 and t = 27.c) The displacement of a particle in space is given by the vector r'(t) = sint cost i+sin²t }+cost k.Find the tangent, the normal and binormal, and the curvature and torsion of the curve atthe points (i) t= 0 and (ii) t = "/2.

Name: Please answer sub c only a) Let the 3-D vector a make angles a, ß and
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: Please answer sub c only a) Let the 3-D vector a make angles a, ß and y with the coordinate axes. Show thatâ = cos ai + cos Bj + cos yk is a unit vector in the direction of the vector a. Show alsothat cos²a + cos?B + cos²y = 1.b) The path of a partic

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c) The displacement of a particle in space is given by the vector 7(t) = sint cost i+sin²t j+cost k. Find the tangent, the normal and binormal, and the curvature and torsion of the curve at the points (i) t= 0 and (ii) t = "/2. %3D