Assuming that b(t)=(b_1(t), b_2(t), b_3(t)) is a vector function, what do each o
ID: 2876498 • Letter: A
Question
Assuming that b(t)=(b_1(t), b_2(t), b_3(t)) is a vector function, what do each of these cases show/mean: (a) b(t) is constant; (b) |b(t)| is constant; (c) b'(t) is constant; (d) |b'(t)| is constant. For b(t) = (R cos(omega, t), R sin(omega, t), 0), where R > 0, omega > 0, find the unit tangent vector T(t). Show that b'(t) is orthogonal to b(t). Also, show that for a vector function with |b(t)| = constant, b'(t) is always orthogonal to b(t). If b(t) = (b_1(t), b_2(t), b_3(t)) is the vector function for the example of the disk rolling around the z-axis on a circle (the equations of which was derived in class), i.e., b(t) = [p cos(t) + b sin(p.t/a) sin(t), p sin(t) - b sin(p.t/a) cos(t),Explanation / Answer
b(t) is a vector depending on the functions b1(t), b2(t), b3(t)
b(t) may or may not be constant depending on b1(t), b2(t), b3(t)
also mod b(t), b'(t) and mod b'(t) may or may not be constant