The lines \frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-k}\; and\; \frac{x-1}{k}=\frac{y-4}{2}=\frac{z-5}{1}\;   are coplanar if

  • Option 1)

    k=1\; or-1

  • Option 2)

    k=0\; or-3

  • Option 3)

    k=3\; or-3

  • Option 4)

    k=0\; or-1

 

Answers (1)
V Vakul

As we leant in

Condition for lines to be intersecting (cartesian form) -

Their shortest distance should be 0

Also the condition for coplanar lines

-

 

 Condition for coplanarity = \begin{vmatrix} 1 &-1 &1 \\ 1& 1& -k\\ k& 2 & 1 \end{vmatrix}= 0

=> k^{2}+3k= 0

k=0   or   -3

 


Option 1)

k=1\; or-1

Incorrect option

Option 2)

k=0\; or-3

Correct option

Option 3)

k=3\; or-3

Incorrect option

Option 4)

k=0\; or-1

Incorrect option

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