Consider a set S_1 = \x = (x_1, x_2, x_3)^T ∈ R^3 x^T x ≤ 16\. Let S_2 be another set which is a subspace of R^3 with dimension two. Which of the following gives the area of S_1 S_2?

GATE DA 2026 Q22: Area where a ball meets a plane through the origin

Linear Algebra
1 mark
MCQ
−1/3 if wrong

Consider a set $S_1 = \{x = (x_1, x_2, x_3)^T \in \mathbb{R}^3 \mid x^T x \le 16\}$ . Let $S_2$ be another set which is a subspace of $\mathbb{R}^3$ with dimension two.

Which of the following gives the area of $S_1 \cap S_2$ ?

Try it: multiple choice: exactly one correct option

Wrong answer costs 1/3 mark in GATE.

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Answer: A (official GATE 2026 final answer key)

Concept used: A 2-dimensional subspace is a plane through the origin; it cuts a ball centred at the origin in a great disc.

First step: $S_1$ is a ball of radius 4, so the intersection is a disc of radius 4.

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Source: official GATE 2026 DA question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key

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GATE DA 2026 Q22: Area where a ball meets a plane through the origin

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