The position vector of a particle moving through space is r(t) = (t − sin t)i + (1 − cost)j + t k, t ≥ 0.

(a) (5 points) Find the velocity and acceleration vectors and the speed as a function of t.

(b) (5 points) Find the parametric equation of the tangent line to the curve described by the particle at t = π/4.

(c) (10 points) Find the time(s) (if any) when the particle’s acceleration vector is orthogonal to its velocity vector.

Please show work.

answer:     true

step-by-step explanation:

solution:

→c= a b , that is product of a and b is possible only when when a is m × n matrix and b is n × p matrix.

that is, number of columns of a= number of rows of b.

so, size of matrix , c= a b is , if a = (m × n)matrix

b= (n × p)matrix

then a b = [ (m × n)matrix] ×[   (n × p)matrix ]

→→c= a b= [m × p ] matrix

→→size of product a b will be equal to = number of rows of a × number of columns of b

if a = 1,   and b = 2, then the answer is 47.99999999. if you round that to the nearest whole number, the answer is 48.