If lines x - 1 2 = y + 1 3 = z - 1 4 and x − 3 1 = y − k 2 = z − 0 1 intersect, then the value of k is

Question

If lines x - 1 2 = y + 1 3 = z - 1 4 and x − 3 1 = y − k 2 = z − 0 1 intersect, then the value of k is, 9 2, 1 2, 5 2, 7 2

MARKS App · Accepted Answer

Given the lines x − 1 2 = y + 1 3 = z − 1 4 and x − 3 1 = y − k 2 = z − 0 1 intersect each other ⇒ | 3 − 1 k + 1 0 − 1 2 3 4 1 2 1 | = 0 ⇒ | 2 k + 1 − 1 2 3 4 1 2 1 | = 0 ⇒ 2 ( − 5 ) − ( k + 1 ) ( − 2 ) − 1 ( 1 ) = 0 ⇒ − 10 + 2 k + 2 − 1 = 0 ⇒ 2 k = 9 ⇒ k = 9 2

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