Consider a Cartesian coordinate system defined over a 3-dimensional vector space with orthogonal unit basis vectors î, ĵ and k̂. Let vector u = √2 î + (1/√2) ĵ + k̂, and vector v = (1/√2) î + √2 ĵ − k̂. The inner product of these vectors (u·v) is:

Question

Accepted Answer

The correct answer is B, 1. GATE 2025 official key: (B). The dot product is the sum of componentwise products: u·v = (√2)(1/√2) + (1/√2)(√2) + (1)(−1) = 1 + 1 − 1 = 1.