Posted by Gunjan kumar on .
Show the two lines (x/21/2)=(y/32/3)=(z/43/4) and (x/54/5)=z intersect.find the point of intersection of these lines

Math 
Reiny,
subbing the 2nd into the first:
x/2  1/2 = z/4  3/4
x/2  1/2 = (1/4)(x/54/5)  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 = 1/43/4
y/3  2/3 = 1
times 3
y  2 = 3
y = 1
they intersect at (1, 1, 1)