Question

Find a vector equation and parametric equations for the line segment that joins P to Q. P(1, -1, 5), Q(5, 6, 1) vector equation r(t) = ? parametric equations (x(t), y(t), z(t)) = ?

Vectors and spaces
ANSWERED
asked 2021-05-07
Find a vector equation and parametric equations for the line segment that joins P to Q.
P(1, -1, 5), Q(5, 6, 1)
vector equation r(t) = ?
parametric equations (x(t), y(t), z(t)) = ?

Expert Answers (1)

2021-05-08
Given points are P(1,-1,5) , Q(5,6,1)
Let a=i-j+5k
b=PQ=(5-1)i+(6+1)j+(1-5)k=4i+7j-4k
The parametric equation of line segment PQ is r(t)=a+tb
r(t)=i-j+5k+t(4i+7j-4k)
r(t)=(1+4t)i+(7t-1)j+(5-4t)k
Where , x=1+4t
y=7t-1
z=5-4t
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