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Question about Lines and planes in Calculus?
Is the line through (-4,6,1) and (-2,0,-3) parallel to the line through (10, 18,4) and (5,3,14) ?
i have no idea where to even begin. i was trying to find each lines parametric equations, but that didnt get me anywhere as far as i know. im lost, please help!
3 Answers
- RobertLv 69 years agoFavorite Answer
Find the direction vectors of the lines.
v1 = <(-2 + 4), (0 - 6), (-3 - 1)> = <2, -6, -4> = 2*<1, -3, -2>
v2 = <(10 - 5), (18 - 3), (4 - 14)> = <5, 15, -10> = 5*<1, 3, -2> = -5*<-1, -3, 2>
Does not appear that the direction vectors are constant multiples of each other, therefore the lines ARE NOT parallel
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- RaffaeleLv 79 years ago
the line AB
A(-4,6,1) B(-2,0,-3)
is parallel to the vector
u = B - A = (2,-6,-4)
the line CD
C(10, 18,4) D(5,3,14)
is parallel to
v = C - D = (5,15,-10)
compute cross product
u⨯v = (120,0,60)
u and v are not parallel because u⨯v is not the null vector
- dennisLv 69 years ago
The equation of the first line is r = (-4, 6, 1) + t(2, -6 ,-4) . (2,- 6,- 4) is obtained by subtracting ( -4, 6,1) from (-2, 0, -3)
The equation of the second line is r = (10, 18, 4) + l(5, 15, - 10).
Since the direction vector (2,- 6,- 4) = (1,-3, -2) and (5, 15, - 10) = (1, 3, -2) are not parallel it follows that the two lines are not parallel.( Two vectors are parallel when one is a multiple of the other.)
