PRECALCULUS:GRAPHICAL,...-NASTA ED.
10th Edition
ISBN: 9780134672090
Author: Demana
Publisher: PEARSON
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Expert Solution & Answer
Chapter 8.6, Problem 43E
Solution
To find: The parametric equations for the line through A and C .
The parametric equations for the line through A and C are x=−1+3t , y=2−6t , and z=4−3t .
Given information:
The given points are A(−1,2,4) and C(2,−4,1) .
Formula used:
If A=(a1,a2,a3) and B=(b1,b2,b3) then vector →AB=(b1−a1,b2−a2,b3−a3) .
If l be a line through point P0(x0,y0,z0) in the direction of a non-zero vector v=〈a,b,c〉 and a point P(x,y,z) is on the line then-
Parametric form of line:- x=x0+at , y=y0+bt and z=z0+ct .
Where t is a real number.
Calculation:
Consider the point A(−1,2,4) and C(2,−4,1) .
The line is in the direction of v=→AC
Using the formula →AB=(b1−a1,b2−a2,b3−a3)
Substitute −1 for a1 , 2 for a2 , 4 for a3 , 2 for b1 , −4 for b2 and 1 for b3 .
→AC=(2−(−1),−4−2,1−4)v=(3,−6,−3)
Parametric equations of line Using the formula x=x0+at , y=y0+bt and z=z0+ct
Substitute −1 for x0 , 2 for y0 , 4 for z0 , 3 for a , −6 for b , −3 for c
x=−1+3t
y=2−6t
z=4−3t
Thus, the parametric equations of the line through A and C are x=−1+3t , y=2−6t , and z=4−3t .
Chapter 8 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
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