   Chapter 12.5, Problem 18E

Chapter
Section
Textbook Problem

# Find parametric equations for the line segment from (−2, 18. 31) to (11. −4, 48).

To determine

To find: The parametric equations for the line segment from (2,18,31) to (11,4,48).

Explanation

Formula used:

The expressions to find the parametric equations for a line through the point P0(x0,y0,z0) and parallel to the direction vector ai+bj+ck is,

x=x0+at,y=y0+bt,z=z0+ct (1)

The expression to find the vector equation [r(t)] for the line segment from the position vectors r0 to r1 is,

r(t)=(1t)r0+tr1,0t1 (2)

The expression for vector equation in terms of position and direction vector is,

r(t)=r0+tv (3)

Here,

r0 is the position vector and

v is the directional vector.

Calculation:

The position vector r0 with the point (2,18,31) is computed as follows.

r0=2i+18j+31k

Write the position vector r1 with the point (11,4,48) is computed as follows.

r1=11i+(4)j+48k=11i4j+48k

The vector equation [r(t)] is computed as follows.

In equation (2), substitute 2i+18j+31k for r0 and 11i4j+48k for r1.

r(t)=(1t)(2i+18j+31k)+t(11i4j+48k),0t1=(2i+18j+31k)t(2i+18j+31k)+t(11i4j+48k),0t1=(2i+18j+31k)+t(2i18

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