Calculus 3 Parametric

Question

A particle moves at a constant speed along a line through P=(4,5,1) to point Q=(9,3,−1). Find the parametric equations and interval for its potions at time t if the particle passes through P at time t=0 and has a constant speed of 3.Give exact answers or round to at least 5 decimal places for x(t),y(t),z(t)

Answer 1

r(t) = <4, 5, 1> + ta<9 - 4, 3 - 5, - 1 - 1> = <4, 5,1> + ta<5, - 2, - 2>;

Ir'(t)I = Ia<5, - 2, - 2> = a√(25 + 4 + 4) = a√33 = 3; a = 3/√33 = √33/11

r(t) = <2, 5, 1> + t√33/11<5, - 2, - 2> ;

x(t) = 2 + 5t√33/11; y(t) = 5 - 2t√33/11; z(t) = 1 - 2t√33/11