The lines x−21=y−31=z−4−k and x−1k=y−42=z−51 are coplanar if-
A
k=1 or −1
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B
k=0 or −3
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C
k=3 or −3
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D
k=0 or −1
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Solution
The correct option is Bk=0 or −3 For two lines to be coplaner, ∣∣
∣∣x2−x1y2−y1z2−z1a1b1c1a2b2c2∣∣
∣∣=0 ⇒∣∣
∣∣−11111−kk21∣∣
∣∣=0⇒−1(1+2k)−1(1+k2)+1(2−k)=0 ⇒k2+3k=0⇒k=0,−3 Hence, option 'B' is correct.