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  • If the lines  <img alt="\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}" src="https://learn.careers360.com/latex-image/?%5Cfrac%7Bx-1%7D%7B2%7D%3D%5Cfrac%7By&plus;1%7D%7B3%7D%3D%5Cfrac%7Bz-1%7D%

If the lines  \frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}  and  \frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1}   intersect, then k is equal to

Option: 1

-1


Option: 2

\frac{2}{9}


Option: 3

\frac{9}{2}


Option: 4

0


Answers (1)

best_answer

As learnt in

Condition for lines to be intersecting (cartesian form) -

Their shortest distance should be 0

Also the condition for coplanar lines

-

 

  

\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}=r_{1}\; and\; \frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1}=r_{2}

or\; 2r_{1}+1=r_{2}+3,3r_{1}-1=2r_{2}+k,4r_{1}+1=r_{2}

\Rightarrow \; 2r_{1}-r_{2}=2\; and\; 4r_{1}-r_{2}=-1

-2r_{1}=3\Rightarrow r_{1}=\frac{-3}{2}\; and\; r_{2}=-5

\therefore \; \; -\frac{9}{2}-1=-10+k\Rightarrow k=10-\frac{11}{2}=\frac{9}{2}

Posted by

Pankaj Sanodiya

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