The line passing through the points (5, 1, a) and (3, b, 1) crosses the yz -plane at the point ≤ft(0, 17/2, -13/2) . Then: - Mathematics MCQ AIEEE 2026 | ExamTest.live

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The line passing through the points (5, 1, a) and (3, b, 1) crosses the yz -plane at the point (0, \frac{17}{2}, - \frac{13}{2}) . Then:

Solution & Step-by-step Explanation

The equation of the line passing through A (5, 1, a) and B (3, b, 1) is: \frac{x - 5}{3 - 5} = \frac{y - 1}{b - 1} = \frac{z - a}{1 - a} \frac{x - 5}{- 2} = \frac{y - 1}{b - 1} = \frac{z - a}{1 - a} = λ The point (0, 17/2, - 13/2) lies on the line.For x = 0 : \frac{0 - 5}{- 2} = λ ⟹ λ = \frac{5}{2} .For y = 17/2 : \frac{17/2 - 1}{b - 1} = \frac{5}{2} ⟹ \frac{15/2}{b - 1} = \frac{5}{2} ⟹ \frac{15}{b - 1} = 5 ⟹ b - 1 = 3 ⟹ b = 4 .For z = - 13/2 : \frac{- 13/2 - a}{1 - a} = \frac{5}{2} ⟹ \frac{- 13 - 2 a}{2 ( 1 - a )} = \frac{5}{2} ⟹ - 13 - 2 a = 5 - 5 a ⟹ 3 a = 18 ⟹ a = 6 .

Try it yourself before checking the explanation above.

The line passing through the points (5, 1, a) and (3, b, 1) crosses the yz -plane at the point (0, \frac{17}{2}, - \frac{13}{2}) . Then:

a = 2, b = 8

a = 4, b = 6

a = 6, b = 4

a = 8, b = 2

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