Please provide detailed explanation of a and b

Question

4. (a) Given that, the displacement vector of a particle is r(t) = (3 sec (5t) + t³)i + (4 csc(5t) + t²)j + (5 cot 3t+t⁴)k, at time t = 0.5 find the magnitude of displacement, speed and the magnitude of acceleration.

(b) Find the curl of V

V = sin(x) cos(y) tan(z)i + x²y²z²j + x⁴y⁴z⁴ k and evaluate its magnitude at x = 0.5, y = 0.7 and z = 0.8.

Answer 1

Take a look at the velocity function

r'(t)= < 15 sec5t tan5t +3t² , −20 csc5t cot 5t +2 t , −15 csc²t + 4t³ >

The calculations are getting out of hand.

Here you need a calculator with CAS , or better do it on Mathematica.