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Find the lenght and equation of the line of shortest distance between the lines x-3/1=y-5/-2=z-7/1 and x+1/7= y+1/-6=z+1/1 Full steps please?

Find the lenght and equation of the line of shortest distance between the lines
 
x-3/1=y-5/-2=z-7/1
and
x+1/7= y+1/-6=z+1/1
 
Full steps please?

Grade:11

1 Answers

Y RAJYALAKSHMI
45 Points
6 years ago
The shortest distance between the lines (x – x1)/l1 = (y – y1)/m1 = (z – z1)/n1
(x – x2)/l2 = (y – y2)/m2 = (z – z2)/n2  is given by
l(x2 – x1) + m(y2 – y1) + n(z2 – z1)  where 
l/(m1n2 – m2n1) = m/(n1l2 – n2l1) = n/(l1m2 – l2m1) = 1/sqrt[1 – (l1l2 + m1m2 + n1n2)2]
 
Substitue the values and simplify
 

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