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MathematicsMultiple correct+3 / -1Question 47 of 60

JEE Advanced 2013 · Paper 2, Mathematics question 47

Two lines L1:x=5, y3−α=z−2L_1:x=5,\ \dfrac y{3-\alpha}=\dfrac z{-2} and L2:x=α, y−1=z2−αL_2:x=\alpha,\ \dfrac y{-1}=\dfrac z{2-\alpha} are coplanar. Then α\alpha can take value(s)

Choose one or more options
Answer and worked solution

Official answer: A, D

Coplanarity. Points (5,0,0)(5,0,0), (α,0,0)(\alpha,0,0); directions (0,3−α,−2)(0,3-\alpha,-2), (0,−1,2−α)(0,-1,2-\alpha):
∣α−50003−α−20−12−α∣=(α−5)[(3−α)(2−α)−2]=(α−5)(α−1)(α−4).\begin{vmatrix}\alpha-5&0&0\\0&3-\alpha&-2\\0&-1&2-\alpha\end{vmatrix}=(\alpha-5)\left[(3-\alpha)(2-\alpha)-2\right]=(\alpha-5)(\alpha-1)(\alpha-4).

Values. α=1\alpha=1 or 44 (and 5).

(A), (D)

Topics:Skew linesScalar and vector triple products
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