Calculus 3 Particles

Question

A particle moves at a constant speed along a line through P=(−8,−4,−9) to point Q=(−3,6,−5). Find the parametric equations for x,y,z its potions at time t if the particle passes through P at time t=2 and through point Q at time t=6.

Answer 1

x = x₁ + ( x₂- x₁)[ (t-t₁)/ (t₂-t₁)]

y = y₁ + ( y₂- y₁)[ (t-t₁)/ (t₂-t₁)]

z = z₁ + ( z₂- z₁)[ (t-t₁)/ (t₂-t₁)]

Then x = - 8 + 5 (t-2 ) / 4

y = - 4 +10 (t-2 ) / 4

z= -9 + 4 (t-2 ) / 4

<5,10,4> is the directing vector of the line and 2 ≤ t ≤ 6