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asked in JEE by (3.7k points)
the shortest distance between the line x-3/3=y/0=z/-4 and the y-axis?
commented by (20.5k points) 1 flag
+1
Is equation given in question valid. Please check again
commented by (3.7k points)
+1
yes...options are given
(a) 1/5
(b) 1
(c) 0
(d) 12/5

1 Answer

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answered by (15 points)

x-3/3=y/0=z/-4=$(let)       (given)

A(3$+3,0,-4$)    is any point on given line

Dc of y axis 0,1,0

Any point on y axis B(0,k,0)

DC of AB 3$+3-0,0-k,-4$-0

For shortest distance

(3$+3)*3+(-k)*0+(-4$)*(-4)=0

So,$=-9/25

Also,

(3$+3)*0+-k*1+(-4$)*0=0

So,k=0

Therefore shortest distance between the lines is distance between 

A(48/25,0,-36/25) and B(0,0,0)

=12/5

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