   Chapter 13.1, Problem 19E

Chapter
Section
Textbook Problem

# Find a vector equation and parametric equations for the line segment that joins P to Q.19. P(0, −1, 1), Q( 1 2 , 1 3 , 1 4 )

To determine

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

Explanation

Given data:

Two vector points P is (0,1,1) and Q is (12,13,14) .

Formula used:

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

r(t)=(1t)r0+tr1for0t1 (1)

Here,

t is parameter.

Consider a vector equation as r(t)=f(t),g(t),h(t) , 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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