If the straight lines x-1/k = y-2/2 = z-3/3 and x-2/3 = y-3/k = z-1/2 intersect at a point, then the integer k is equal to: - Mathematics MCQ AIEEE 2026 | ExamTest.live

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If the straight lines \frac{x - 1}{k} = \frac{y - 2}{2} = \frac{z - 3}{3} and \frac{x - 2}{3} = \frac{y - 3}{k} = \frac{z - 1}{2} intersect at a point, then the integer k is equal to:

Solution & Step-by-step Explanation

If two lines \frac{x - x _{1}}{a _{1}} = \frac{y - y _{1}}{b _{1}} = \frac{z - z _{1}}{c _{1}} and \frac{x - x _{2}}{a _{2}} = \frac{y - y _{2}}{b _{2}} = \frac{z - z _{2}}{c _{2}} intersect, then: x_{2} - x_{1} a_{1} a_{2} y_{2} - y_{1} b_{1} b_{2} z_{2} - z_{1} c_{1} c_{2} = 0 2 - 1 k 3 3 - 2 2 k 1 - 3 32 = 0 ⟹ 1 k 3 12 k - 2 32 = 0 Expanding along the first row: 1 (4 - 3 k) - 1 (2 k - 9) - 2 (k^{2} - 6) = 0 4 - 3 k - 2 k + 9 - 2 k^{2} + 12 = 0 - 2 k^{2} - 5 k + 25 = 0 ⟹ 2 k^{2} + 5 k - 25 = 0 (2 k - 5) (k + 5) = 0 k = 5/2 or k = - 5 .Since k is an integer, k = - 5 .

Try it yourself before checking the explanation above.

If the straight lines \frac{x - 1}{k} = \frac{y - 2}{2} = \frac{z - 3}{3} and \frac{x - 2}{3} = \frac{y - 3}{k} = \frac{z - 1}{2} intersect at a point, then the integer k is equal to:

- 5

5

2

- 2

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