Two lines L 1  :  x = 5 , y 3 - α = z - 2 and L 2  :  x = α , y - 1 = z 2 - α are coplanar. Then α can take value(s)

Question

Two lines L 1 &#160;:&#160; x = 5 , y 3 - &#945; = z - 2 and L 2 &#160;:&#160; x = &#945; , y - 1 = z 2 - &#945; are coplanar. Then &#945; can take value(s)

Aicharya · Accepted Answer

$\frac{x-5}{0} = \frac{-y}{\alpha-3} = \frac{z}{-2}$ $\frac{x-\alpha}{0} = \frac{y}{-1}= \frac{z}{2-\alpha}$ $\begin{vmatrix} 5-\alpha & 0 & 0 \ 0 & 3-\alpha & -2 \ 0 & -1 & 2-\alpha \end{vmatrix} = 0$ $(5-\alpha) \cdot ((3-\alpha) \cdot (2-\alpha) - 2) = 0$ $(\alpha - 5) \cdot (\alpha^2 - 5\alpha + 6 - 2) = 0$ $(\alpha - 5) \cdot (\alpha^2 - 5\alpha + 4) = 0$ $\alpha = 1, 4, 5$

Two lines L 1  :  x = 5 , y 3 - α = z - 2 and L 2  :  x = α , y - 1 = z 2 -…

Solution

Two lines L 1 &#160;:&#160; x = 5 , y 3 - &#945; = z - 2 and L 2 &#160;:&#160; x = &#945; , y - 1 = z 2 -…

Solution

Two lines L 1 : x = 5 , y 3 - α = z - 2 and L 2 : x = α , y - 1 = z 2 -…