Vector Algebra

JEE Main · Mathematics · 10 past questions

These are the board's own papers. 211 more board questions reprinted in the books we use in class are for signed-in students: sign in.

1. Q1 2026 2 Apr Shift 1

   If $\vec{a}$ and $\vec{b}$ are two vectors such that $|\vec{a}|=2$ and $|\vec{b}|=3$, then the maximum value…

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2. Q2 2026 2 Apr Shift 2

   Let the vectors $\vec{a} = -\hat{i} + \hat{j} + 3\hat{k}$ and $\vec{b} = \hat{i} + 3\hat{j} + \hat{k}$. For…

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3. Q3 2026 2 Apr Shift 2

   Two adjacent sides of a parallelogram PQRS are given by $\overrightarrow{PQ} = \hat{j} + \hat{k}$ and…

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4. Q4 2026 4 Apr Shift 1

   Let $\vec{a}_k = (\tan\theta_k)\hat{i}+\hat{j}$ and $\vec{b}_k=\hat{i}-(\cot\theta_k)\hat{j}$, where…

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5. Q5 2026 4 Apr Shift 2

   Let $\hat u$ and $\hat v$ be unit vectors inclined at an acute angle such that…

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6. Q6 2026 5 Apr Shift 1

   Let $\vec a = \sqrt7\hat i + \hat j - \hat k$ and $\vec b = \hat j + 2\hat k$. If $\vec r$ is a vector such…

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7. Q7 2026 5 Apr Shift 2

   Let O be the origin, $\overrightarrow{OP} = \vec{a}$ and $\overrightarrow{OQ} = \vec{b}$. If R is the point…

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8. Q8 2026 6 Apr Shift 1

   If $\vec a=\hat i+\hat j+\hat k$, $\vec b=\hat j-\hat k$ and $\vec c$ be three vectors such that…

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9. Q9 2026 6 Apr Shift 2

   Let $\vec{a}=2\hat{i}+3\hat{j}+3\hat{k}$ and $\vec{b}=6\hat{i}+3\hat{j}+3\hat{k}$. Then the square of the…

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10. Q10 2026 8 Apr Shift 2

    Let a = 4i-j+3k, b=10i+2j-k and a vector c be such that 2(a×b)+3(b×c)=0. If a·c = 15, then c·(i+j-3k) is…

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