If for some \alpha \in R, the lines L_1 : \frac{x+1}{2} = \frac{y-2}{-1} = \frac{z - 1}{1} and L_2 : \frac{x+2}{\alpha} = \frac{y+1}{5-\alpha} = \frac{z + 1}{1} are coplanar then the line L2 passes through the point:  
Option: 1 (2,-10, -2)   
Option: 2  (10,2,2)   
Option: 3 10,-2,-2)     
Option: 4  (-2,10,2)

Answers (1)

Given equations of line 

L_1 : \frac{x+1}{2} = \frac{y-2}{-1} = \frac{z - 1}{1}

L_2 : \frac{x+2}{\alpha} = \frac{y+1}{5-\alpha} = \frac{z + 1}{1}

For the coplanarity of two lines

\\\begin{vmatrix} -1+2 &2+1 &1+1 \\ 2 &-1 &1 \\ \alpha& 5-\alpha & 1 \end{vmatrix}=0\\1(-1-5+\alpha)-3(2-\alpha)+2(10-2\alpha+\alpha)=0\\\alpha=-4

Now

\\\L_2:\frac{x+2}{-4}=\frac{y+1}{9}=\frac{z+1}{1}\\\text{point }(2,-10,-2)\;\text{satisfy the equation.}

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