Asked by Gunjan kumar
Show the two lines (x/2-1/2)=(y/3-2/3)=(z/4-3/4) and (x/5-4/5)=z intersect.find the point of intersection of these lines
Answers
Answered by
Reiny
subbing the 2nd into the first:
x/2 - 1/2 = z/4 - 3/4
x/2 - 1/2 = (1/4)(x/5-4/5) - 3/4
times 4
2x - 2 = (x/5 - 4/5) - 3
times 5
10x - 10 = x - 4 - 15
9x = -9
x = -1
into z = x/5 - 4/4 = -1/5 - 4/5 = -1
z = -1
lastly
y/3 - 2/3 = z/4 - 3/4
y/3 - 2/3 = -1/4-3/4
y/3 - 2/3 = -1
times 3
y - 2 = -3
y = -1
they intersect at (-1, -1, -1)
x/2 - 1/2 = z/4 - 3/4
x/2 - 1/2 = (1/4)(x/5-4/5) - 3/4
times 4
2x - 2 = (x/5 - 4/5) - 3
times 5
10x - 10 = x - 4 - 15
9x = -9
x = -1
into z = x/5 - 4/4 = -1/5 - 4/5 = -1
z = -1
lastly
y/3 - 2/3 = z/4 - 3/4
y/3 - 2/3 = -1/4-3/4
y/3 - 2/3 = -1
times 3
y - 2 = -3
y = -1
they intersect at (-1, -1, -1)
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