GATE Engineering Mathematics: Vector Calculus – Previous Year Questions

8 GATE previous year questions on Vector Calculus (Engineering Mathematics, Mining Engineering) with answers and explanations, from every paper.

1. GATE 2021 MN Q18 (1 mark, Multiple choice) – For the coplanar vectors shown, let c=( a+ b)( a- b). Its magnitude equals which quantity?
2. GATE 2022 MN Q12 (1 mark, Multiple choice) – A velocity field is v=x i+y j+p(z) k, with p(0)=0. If its divergence is zero, find p(z).
3. GATE 2022 MN Q14 (1 mark, Multiple choice) – For the vectors x and y shown, which expression is the vector projection of x onto nonzero y?
4. GATE 2023 MN Q14 (1 mark, Multiple choice) – Given A=3 i+2 j and B= i+ j, find the magnitude of the projection of A along B.
5. GATE 2024 MN Q26 (1 mark, Multiple choice) – Find F for F=2x i+3y j+4z k.
6. GATE 2024 MN Q43 (2 marks, Multiple choice) – Triangle sides are a=(2, 3, −4), b=(4, 2, 3). Find triangle area and a unit normal.
7. GATE 2025 MN Q56 (2 marks, Numerical answer) – Find the directional derivative of f=4x2+8y2+9z2 at(3,4,5),along 2 i-3 j+4 k,to one decimal.
8. GATE 2026 MN Q12 (1 mark, Multiple choice) – Find the divergence of F=x2y i+y3x j at (3,2).