At time t equals0, a particle is located at the point (5,2,7). It travels in a straight line to the point (8,1,6), has speed 4 at (5,2,7) and constant acceleration 3 I - J- K. Find an equation for the position vector r(t) of the particle at time t.

Step-by-step explanation:

First, we integrate the acceleration fiction to obtain the velocity function.

The acceleration function, 3i - j - k, in vector form is

So,  

Where is a constant vector. To obtain , knowing that the particle has speed 4 at (5, 2, 7) at t = 0.

= 4

The particle travels in a straight line to (8, 1, 6), and (8, 1, 6) - (5, 2, 7) =

There is a constant, s, such that

So,

Therefore,

and

Next,  we find the position function by integrating the velocity function.

Where is a constant vector. To obtain , knowing that the particle is at (5, 2, 7) at t = 0.

(a) the volume of the cone is 20/3 in3

hence, option a is correct.