PRECALCULUS:GRAPHICAL,...-NASTA ED.
10th Edition
ISBN: 9780134672090
Author: Demana
Publisher: PEARSON
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Expert Solution & Answer
Chapter 8, Problem 74RE
Solution
To find: The parametric equations for the line in the direction of w through the midpoint of P(−1,0,3) and Q(3,−2,−4) .
The equations are x=1+3t,y=−1−4t,z=−12
Given information:
w=〈3,−4,0〉
P(−1,0,3)
Q(3,−2,−4) .
Formula used:
The midpoint M of the line segment PQ with endpoints P(x1,y1,z1) and Q(x2,y2,z2) is M=(x1+x22,y1+y22,z1+z22) .
If l is a line through the point P0(x0,y0,z0) in the direction of a nonzero vector v=〈a,b,c〉 , then a point P(x,y,z) is on l then the parametric equation are x=x0+at,y=y0+bt, and z=z0+ct .
Calculation:
Substitute −1 for x1 , for y1 , 3 for z1 , 3 for x2 , −2 for y2 and −4 for z2 in the midpoint formula.
M=(−1+32,0−22,3−42)=(22,−22,−12)=(1,−1,−12)
Substitute 1 for x0 , −1 for y0 , −12 for z0 , 3 for a , −4 for b and 0 for c in the formula to form parametric equation.
x=1+3ty=−1−4tz=−12+0t
Hence, the parametric equations are x=1+3t,y=−1−4t,z=−12
Chapter 8 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
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