JEE Main Mathematics: Coplanar lines Practice Questions
7 free multiple-choice questions on Coplanar lines (Analytical Geometry) for JEE Main Mathematics, each with the correct answer and a step-by-step explanation. Attempt a question, then reveal the solution to check your reasoning.
Practice thousands more JEE Main questions in the app →Q1. If two lines are perpendicular to the same line, then the two lines are:
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Correct answer: A — Perpendicular
If two lines are perpendicular to the same line, they must be parallel to each other. If L₁ ⊥ L and L₂ ⊥ L, then L₁ || L₂.
Q2. Consider two lines l₁: 2x + 3y - 5 = 0 and l₂: 4x + 6y - 10 = 0. Are these lines parallel or coincident?
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Correct answer: B — Coincident
The ratio of the coefficients of x and y in both equations is equal (2/4 = 1/2, 3/6 = 1/2, -5/-10 = 1/2). Thus, the lines are coincident (coincident).
Q3. Consider the lines l₁: x + y + 1 = 0 and l₂: 2x + 2y + 3 = 0. These lines are:
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Correct answer: A — Parallel
The slopes are m₁ = -1/1 = -1 and m₂ = -2/2 = -1. Since the slopes are equal (m₁ = m₂), the lines are parallel. (Since 1/1 ≠ 2/2, they are distinct parallel lines).
Q4. Two lines, 3x + 2y + 5 = 0 and 6x + 4y - 1 = 0, are:
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Correct answer: B — Coincident
The slope of the first line is m₁ = -3/2. The slope of the second line is m₂ = -6/4 = -3/2. Since the slopes are equal, the lines are parallel. (They are not coincident as the constant terms differ).
Q5. If two lines l₁: 5x - 2y + 1 = 0 and l₂: 10x - 4y + 5 = 0 are given, what is the relationship between them?
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Correct answer: C — The lines are parallel
To check for parallelism, we compare the ratios of the coefficients of x and y. a₁/a₂ = 5/10 = 1/2 and b₁/b₂ = -2/-4 = 1/2. Since a₁/a₂ = b₁/b₂, the lines are parallel.
Q6. If three lines l₁, l₂, and l₃ intersect pairwise, the condition for them to be coplanar is that the area of the triangle formed by these lines is zero. This implies what about the intersection points?
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Correct answer: A — The intersection points must be collinear
If three lines are coplanar and intersect pairwise, they form a triangle unless they are all concurrent (intersect at a single point). For them to be coplanar, they must reside in the same plane.
Q7. Three lines l₁: 2x + 3y - 5 = 0, l₂: 4x + 6y - 10 = 0, and l₃: 5x + 9y + 2 = 0 are given. If the lines are parallel, then the relationship between their coefficients is:
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Correct answer: B — 2:3:5
For three lines to be parallel, the ratio of their corresponding coefficients must be equal. If l₁ and l₂ are parallel, then 2/4 = 3/6 = (-5)/(-10) = 1/2. The condition for all three lines to be parallel is l₁:l₂:l₃. Since l₁ and l₂ are parallel, the ratios are equal.
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