Question

Find a vector equation and parametric equations for the line segment that joins P to Q. P(0, - 1, 1), Q(1/2, 1/3, 1/4)

Vectors
ANSWERED
asked 2021-05-29
Find a vector equation and parametric equations for the line segment that joins P to Q.
P(0, - 1, 1), Q(1/2, 1/3, 1/4)

Answers (1)

2021-05-30
Vector equation of a line segment joining the points with position vectors \(r_0\) and \(r_1\) is
\(r=(1-t)r_0+tr_1\)
Where \(t\in[0,1]\)
Substitute \(r_0=<0,-1,1>\) and \(r_1=<\frac{1}{2}.\frac{1}{3},\frac{1}{4}>\)
\(r(t)=(1-t)(0,-1,1)+t<\frac{1}{2},\frac{1}{3},\frac{1}{4}>\)
\(r(t)=<0,-1+t,1-t>+<\frac{t}{2},\frac{t}{3},\frac{t}{4}>\)
\(r(t)=<\frac{t}{2},-1+\frac{4t}{3},1-\frac{3t}{4}>\)
Where \(t\in[0,1]\) The parametric equations for the line segment are
\(x=\frac{t}{2},y=-1+\frac{4t}{3},z=1-\frac{3t}{4}\)
Where \(t\in[0,1]\)
0
 
Best answer

expert advice

Have a similar question?
We can deal with it in 3 hours
...