If the straight lines x−1k=y−22=z−33 and x−23=y−3k=z−13 intersect at a point, then the integer k is equal to
A
−2
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B
−5
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C
5
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D
2
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Solution
The correct option is A−5 Given, two lines intersect at a point. Therefore, the shortest distance between them is zero. ∴∣∣
∣∣k233k211−2∣∣
∣∣=0 ⇒k(−2k−2)−2(−6−2)+3(3−k)=0 ⇒2k2+5k−25=0 ⇒(2k−5)(k+5)=0 ⇒k=52,−5 Hence, integer value of k is −5.