JEE Advanced · 2007 · 08 Apr 2007 · Paper 1 · Vector Algebra

More JEE Advanced questions on Vector Algebra

1. For real numbers $\alpha ,\beta ,\gamma ,\delta$ and $\mu$, consider the matrix
   

   $$M=\left[\begin{array}{ccc}\alpha & \frac{1}{\sqrt{2}}& -\frac{1}{\sqrt{2}}\\ \frac{1}{\sqrt{3}}& \beta & \frac{1}{\sqrt{3}}\\ \gamma & \delta & \mu \end{array}\right]$$

   
   Suppose that …
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2. Let $\vec{a},\vec{b}$ be two vectors, and let P, Q and R be the points with position vectors $\vec{a},\vec{b}$ and $\vec{a}+\vec{b}$, respectively, with respect to the origin O. If …
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3. For any two points $M$ and $N$ in the $XY$-plane, let $\overrightarrow{MN}$ denote the vector from $M$ to $N$, and $\overrightarrow{0}$ denote the zero vector. Let $P,Q$ and $R$ be three distinct points in the $XY$-plane. Let $S$ be a point inside the tr …
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4. Let $\vec{w}=\hat{i}+\hat{j}-2\hat{k}$, and $\overrightarrow{\mathrm{u}}$ and $\overrightarrow{\mathrm{v}}$ be two vectors such that $\vec{u}\times \vec{v}=\vec{w}$ and $\vec{v}\times \vec{w}=\vec{u}$. Let $\alpha ,\beta ,\gamma$ and $t$ be real numbers such that …
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5. Consider the vectors
   

   $$\vec{x}=\hat{i}+2\hat{j}+3\hat{k},\vec{y}=2\hat{i}+3\hat{j}+\hat{k},\text{ and }\vec{z}=3\hat{i}+\hat{j}+2\hat{k}$$

   
   For two distinct positive real numbers $\alpha$ and $\beta$, define …
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6. Let $\vec{p}=2\hat{i}+\hat{j}+3\hat{k}$ and $\vec{q}=\hat{i}-\hat{j}+\hat{k}$. If for some real numbers $\alpha ,\beta$ and $\gamma$, we have
   

   $$15\hat{i}+10\hat{j}+6\hat{k}=\alpha (2\vec{p}+\vec{q})+\beta (\vec{p}-2\vec{q})+\gamma (\vec{p}\times \vec{q}),$$

   
   then the value of …
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