GATE DA 2026 Set 1 — Question 22
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Linear Algebra → Vector Algebra → Norms (L1, L2, Lp, Max)
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Question
Consider a set . Let be another set which is a subspace of with dimension two.Which of the following gives the area of ?
Correct answer
(A) 16π
Solution
The set is defined by , which corresponds to , or . This represents a solid sphere (ball) in centered at the origin with radius .The set is a subspace of with dimension two. Geometrically, a 2-dimensional subspace of is a plane passing through the origin.The intersection is the intersection of a solid sphere of radius 4 and a plane passing through its center. This intersection is a 2-dimensional disk of radius .The area of this disk is given by:Thus, the correct option is (A).
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