Chapter 13.1, Problem 18E

### Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

Chapter
Section

### Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

# Find a vector equation and parametric equations for the line segment that joins P to Q.18. P(−1, 2, −2), Q(−3, 5, 1)

To determine

To find: the vector equation and parametric equation of line segment P to Q.

Explanation

Given data:

Two vector points P is (âˆ’1,2,âˆ’2) and Q is (âˆ’3,5,1) .

Formula used:

Write the expression for line segment from two vectors r0 to r1 (r(t)) .

r(t)=(1âˆ’t)r0+tr1â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰forâ€‰0â‰¤tâ‰¤1 (1)

Here,

t is parameter.

Consider a vector equation as r(t)=âŒ©f(t),g(t),h(t)âŒª , then parametric equations to plot space curve C are,

x=f(t)y=g(t)z=h(t)

Here,

f(t) , g(t) , and h(t) are component functions of r (t), and

x, y, and z are parametric equations of C.

Find the line segment (r(t)) joining P to Q by the use of equation (1)

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