Sub-topic 1
2025 · National One-Eighth
Free
Scalar product of $\mathbf{a}+\mathbf{b}$ and $\mathbf{a}-\mathbf{b}$ using $|\mathbf{a}|^2-|\mathbf{b}|^2$
Read past contest →
Sub-topic 2
2025 · National One-Eighth
Premium
$(a+b)\cdot(a-b)$ for $a=2i+3j$ and $b=4i-3j$
Read past contest →
Sub-topic 3
2024 · National Preliminary
Premium
Meaning of $\mathbf{a}\cdot\mathbf{b}=0$ for non-zero vectors (true/false)
Read past contest →
Sub-topic 4
2024 · National Preliminary
Premium
Vector of length $65$ in the direction of $5\mathbf{i}-12\mathbf{j}$
Read past contest →
Sub-topic 5
2026 · National Preliminary
Premium
Sine of the angle between $2\mathbf{i}+\mathbf{j}$ and $\mathbf{i}-\mathbf{j}$
Read past contest →
Sub-topic 6
2025 · National Preliminary
Premium
Sine of the angle between $2\mathbf{i}+3\mathbf{j}$ and $3\mathbf{i}+2\mathbf{j}$
Read past contest →
Sub-topic 7
2026 · National Preliminary
Premium
Sine of the angle between $2\mathbf{i}+\mathbf{j}$ and $\mathbf{i}-\mathbf{j}$ (formula method)
Read past contest →
Sub-topic 8
2026 · National Preliminary
Premium
Component of $5\mathbf{i}+6\mathbf{j}$ in the direction of $3\mathbf{i}+4\mathbf{j}$
Read past contest →
Sub-topic 9
2026 · National Preliminary
Premium
Tangent of the angle between $2\mathbf{i}+\mathbf{j}$ and $\mathbf{i}+2\mathbf{j}$
Read past contest →
Sub-topic 10
2026 · National Quarterfinal
Premium
Locus of $p(x,y)$ when $2x\mathbf{i}+y\mathbf{j}$ and $x\mathbf{i}-2y\mathbf{j}$ are perpendicular
Read past contest →
Sub-topic 11
2026 · National Quarterfinal
Premium
Tangent of the angle between $5\mathbf{i}+\mathbf{j}$ and $5\mathbf{i}-\mathbf{j}$
Read past contest →
Sub-topic 12
2026 · National One-Eighth
Premium
Locus of $p(x,y)$ when $2x\mathbf{i}+y\mathbf{j}$ and $x\mathbf{i}-2y\mathbf{j}$ are perpendicular (speed race)
Read past contest →
Sub-topic 13
2018 · National One-Eighth
Premium
Value of $x$ when $|x\mathbf{i}+7\mathbf{j}|=25$
Read past contest →
Sub-topic 14
2025 · National Quarterfinal
Premium
Sine of the angle between $3\mathbf{i}+\mathbf{j}$ and $\mathbf{i}-2\mathbf{j}$
Read past contest →
Sub-topic 15
2025 · National Quarterfinal
Premium
Tangent of the angle between $4\mathbf{i}+2\mathbf{j}$ and $2\mathbf{i}+4\mathbf{j}$
Read past contest →
Sub-topic 16
2023 · National One-Eighth
Premium
Vector of magnitude $10$ in the direction of $\mathbf{i}+\sqrt{3}\mathbf{j}$
Read past contest →
Sub-topic 17
2021 · National One-Eighth
Premium
Magnitudes of $2a-b$, $3a+3b$, $a+2b$ for $a=2i+j$, $b=i-3j$
Read past contest →
Sub-topic 18
2024 · National One-Eighth
Premium
Magnitude of $3\mathbf{a}+2\mathbf{b}$ for $\mathbf{a}=3\mathbf{i}-2\mathbf{j}$, $\mathbf{b}=2\mathbf{i}+3\mathbf{j}$
Read past contest →
Sub-topic 19
2024 · Regional Championship
Premium
Vector from $a(-3,2)$ to $b(2,-6)$ in terms of $\mathbf{i}$ and $\mathbf{j}$
Read past contest →
Sub-topic 20
2025 · National Preliminary
Premium
Value of $k$ making $2\mathbf{a}+k\mathbf{b}$ or $k\mathbf{a}+2\mathbf{b}$ parallel to $\mathbf{i}$ or $\mathbf{j}$
Read past contest →
Sub-topic 21
2024 · National Preliminary
Premium
What $\mathbf{a}\cdot\mathbf{b}=0$ implies about two vectors (true/false)
Read past contest →
Sub-topic 22
2013 · National Preliminary
Premium
Properties of vectors and the scalar product (true/false)
Read past contest →
Sub-topic 23
2013 · National Preliminary
Premium
Vector of length $10$ parallel to $2\mathbf{i}-2\mathbf{j}$
Read past contest →
Sub-topic 24
2013 · National Preliminary
Premium
Vector of length $10$ perpendicular to $3\mathbf{i}+4\mathbf{j}$
Read past contest →
Sub-topic 25
2013 · National Preliminary
Premium
Scalar product of $5\mathbf{i}-7\mathbf{j}$ and $14\mathbf{i}+10\mathbf{j}$
Read past contest →
Sub-topic 26
2021 · National Preliminary
Premium
Value of $k$ for which $3\mathbf{i}-k\mathbf{j}$ and $12\mathbf{i}+k\mathbf{j}$ are perpendicular
Read past contest →
Sub-topic 27
2021 · National Preliminary
Premium
Velocity from the position vector $\mathbf{r}=at^2\mathbf{i}+bt\mathbf{j}$
Read past contest →
Sub-topic 28
2021 · National Preliminary
Premium
Value of $x$ when $|5\mathbf{i}+x\mathbf{j}|=13$
Read past contest →
Sub-topic 29
2021 · National Quarterfinal
Premium
Cosine of the angle between $12\mathbf{i}-5\mathbf{j}$ and $4\mathbf{i}+3\mathbf{j}$
Read past contest →
Sub-topic 30
2021 · National Quarterfinal
Premium
Bearing of the direction of the vector $\mathbf{i}-\mathbf{j}$
Read past contest →
Sub-topic 31
2023 · National One-Eighth
Premium
Final velocity $\mathbf{v}=\mathbf{u}+\mathbf{a}t$ (three examples)
Read past contest →
Sub-topic 32
2023 · National Quarterfinal
Premium
Angular momentum $\mathbf{l}=\mathbf{r}\times m\mathbf{v}$ of a $3$ kg particle
Read past contest →
Sub-topic 33
2023 · National Quarterfinal
Premium
Vector of magnitude $10$ in the direction of $\mathbf{i}+\sqrt{3}\mathbf{j}$ (second copy)
Read past contest →