prove that a line through A(0,-1,-1) and coordinate B(4,5,1) intersect the line through C(3,9,4) and D(-4,4,4)
Anonymous:
Do you want a more generalized proof (which is difficult to type on this thing) or would a easier one suffice?
They actually intersect at (10,14,4).
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I will use the parametric representation of a line
in 3-dimensions using a vector and a point on the line, to solve
this. There could be other ways.
vector AB = 4 i + 6 j + 2 k vector CD = 7 i - 5 j + 0 k
parametric representation of line AB with point A (0, -1, -1) on it :
x = 0 + 4 t , y = -1 + 6 t , z = -1 + 2 t
That of line CD is with point C is,
x = 3 + 7 s y = 9 - 5 s z = 4 + 0 s
Solve these pairs of equations to get t and s.
s = -1 , t = 5/2
Point of intersection is (10, 14, 4)
vector AB = 4 i + 6 j + 2 k vector CD = 7 i - 5 j + 0 k
parametric representation of line AB with point A (0, -1, -1) on it :
x = 0 + 4 t , y = -1 + 6 t , z = -1 + 2 t
That of line CD is with point C is,
x = 3 + 7 s y = 9 - 5 s z = 4 + 0 s
Solve these pairs of equations to get t and s.
s = -1 , t = 5/2
Point of intersection is (10, 14, 4)
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