Find a parametric equation for the position of the particle

Find a parametric equation for the position of the particle in terms of the parameter

t.

Solution

r(t) = r1 + v*t r(t) = r1 + (-1,4,1)*t now, at t=5 ,r(t)= (-1,-4,-2) putting the values, r1 = (-1,-4,-2) - (-1,4,1)*5 = (-1,-4,-2) - (-5,20,5) = (4,-24,-7) therefore, r(t) = (4,-24,-7) + (-1,4,1)*t