Exams › JEE Main › Maths

A tetrahedron is formed by the points O(0, 0, 0), A(1, 2, 1), B(2, 1, 3), and C(−1, 1, 2). The angle between the planes OAB and ABC is

1. 90°
2. cos−1(19/35)
3. cos−1(17/31)
4. 30°

Correct answer: cos−1(19/35)

Solution

The angle between two planes can be determined using the normal vectors of the planes. By calculating the normal vectors for planes OAB and ABC and then using the dot product formula, we find that the angle between these planes is cos−1(19/35), confirming option B as the correct answer.

Related JEE Main Maths questions

• Consider the following two statements: Statement 1: If A, B and C are points with position vectors a = 2î + ĵ + k̂, b = 3î - ĵ + 3k̂ and c = î + 7ĵ - 5k̂, then the figure OABC forms a tetrahedron. Statement 2: If the position vectors a, b and c of points A, B and C are non-coplanar, then OABC is a tetrahedron, where O denotes the origin. Choose the correct option.
• A moving plane always contains the fixed point (1, 2, 3). The set of points that are the perpendicular projections of the origin onto this plane is described by
• The direction cosines l, m, n of one of the two lines satisfying the relations l - 5m + 3n = 0 and 7l² + 5m² - 3n² = 0 are
• A straight line is equally inclined to the x-axis and the y-axis, making an angle α with each. If its angle θ with the z-axis satisfies sin²θ = 2 sin²α, determine α.
• Let Q be the reflection of the point P(2, 3, 4) across the plane x − 2y + 5z = 6. The equation of the line joining P and Q is
• Find the point where the perpendicular drawn from the point (2, 4, −1) meets the line x + 5 = (1/4)(y + 3) = (−1/9)(z − 6).

⚔️ Practice JEE Main Maths free + battle 1v1 →