JEE Main · 2023 · 29 Jan 2023 · Shift 1 · Vector Algebra

More JEE Main questions on Vector Algebra

1. Let $\vec{a}=-\hat{i}+2\hat{j}+2\hat{k},\vec{b}=8\hat{i}+7\hat{j}-3\hat{k}$ and $\vec{c}$ be a vector such that $\overrightarrow{\mathrm{a}}\times \overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{b}}$. If …
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2. Let $\overrightarrow{\mathrm{c}}$ and $\overrightarrow{\mathrm{d}}$ be vectors such that $|\overrightarrow{\mathrm{c}}+\overrightarrow{\mathrm{d}}|=\sqrt{29}$ and …
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3. For a triangle $ABC$, let $\vec{p}=\overrightarrow{BC},\vec{q}=\overrightarrow{CA}$ and $\overrightarrow{\mathrm{r}}=\overrightarrow{\mathrm{BA}}$. If $|\overrightarrow{\mathrm{p}}|=2\sqrt{3},|\overrightarrow{\mathrm{q}}|=2$ and $\cos \theta =\frac{1}{\sqrt{3}}$, where $\theta$ …
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4. Let $\overrightarrow{AB}=2\hat{i}+4\hat{j}-5\hat{k}$ and $\overrightarrow{\mathrm{AD}}=\hat{\mathrm{i}}+2\hat{\mathrm{j}}+\lambda \hat{k},\lambda \in \mathbb{R}$. Let the projection of the vector …
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5. Let $\vec{a}=2\hat{i}-\hat{j}+\hat{k}$ and $\vec{b}=\lambda \hat{j}+2\hat{k}$, $\lambda \in \mathbb{Z}$ be two vectors. Let $\vec{c}=\vec{a}\times \vec{b}$ and $\vec{d}$ be a vector of magnitude 2 in yz-plane. If $|\vec{c}|=\sqrt{53}$, then the maximum p …
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6. Let a vector $\vec{a}=\sqrt{2}\hat{i}-\hat{j}+\lambda \hat{k},\lambda >0$, make an obtuse angle with the vector $\vec{b}=-{\lambda }^2\hat{i}+4\sqrt{2}\hat{j}+4\sqrt{2}\hat{k}$ and an angle $\theta ,\frac{\pi }{6}<\theta <\frac{\pi }{2}$, with the positive $z$-axis. If …
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