Question

Find a function r(t) that describes the line passing through Upper P (5,6,7) and Q(9,8,2).

Answer 1

r(t)= (5,6,7) + (4,2,-5)*t

Explanation:

one way to describe the line r is though parametric equations r(t), where

r(t)= P₀(x₀,y₀) + v(x₁,y₁)*t

where

P₀(x₀,y₀)= any point that lies on the line = P(5,6,7)

v= vector parallel to the line = Q(9,8,2) - P(5,6,7) = (4,2,-5)

then

r(t)= (5,6,7) + (4,2,-5)*t

to verify it:

if t=0 →r(0)=P(5,6,7)

if t=1 →r(1)= Q(9,8,2)