Vector Algebra · JEE Main previous year questions

2002 6 questions

1. Q282002 · 27 Apr 2002 · Shift 1

   $I_n={\int }_0^{\pi /4}{\tan }^{n}xdx$ then ${\lim }_{n\to \infty }n[I_n+I_{n+2}]$ equals

   1. A.$\frac{1}{2}$
   2. B.$1$
   3. C.$\infty$
   4. D.zero
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   Answer: B

2. Q372002 · 27 Apr 2002 · Shift 1

   If $|\vec{a}|=4,|\vec{b}|=2$ and the angle between $\vec{a}$ and $\vec{b}$ is $\pi /6$ then $(\vec{a}\times \vec{b}{)}^2$ is equal to :

   1. A.$48$
   2. B.$16$
   3. C.$\vec{a}$
   4. D.none of these
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   Answer: B

3. Q382002 · 27 Apr 2002 · Shift 1

   If the vectors $\vec{\mathbf{a}},\vec{\mathbf{b}}$ and $\vec{\mathbf{c}}$ form the sides $BC,CA$ and $AB$ respectively of a triangle $ABC$, then :

   1. A.$\vec{\mathbf{a}}\cdot \vec{\mathbf{b}}+\vec{\mathbf{b}}\cdot \vec{\mathbf{c}}+\vec{\mathbf{c}}\cdot \vec{\mathbf{a}}=0$
   2. B.$\vec{\mathbf{a}}\times \vec{\mathbf{b}}=\vec{\mathbf{b}}\times \vec{\mathbf{c}}=\vec{\mathbf{c}}\times \vec{\mathbf{a}}$
   3. C.$\vec{\mathbf{a}}\cdot \vec{\mathbf{b}}=\vec{\mathbf{b}}\cdot \vec{\mathbf{c}}=\vec{\mathbf{c}}\cdot \vec{\mathbf{a}}=0$
   4. D.$\vec{\mathbf{a}}\times \vec{\mathbf{b}}+\vec{\mathbf{b}}\times \vec{\mathbf{c}}+\vec{\mathbf{c}}\times \vec{\mathbf{a}}=\vec{0}$
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   Answer: B

4. Q402002 · 27 Apr 2002 · Shift 1

   If the vectors $\vec{c},\vec{a}=x\hat{i}+y\hat{j}+z\hat{k}$ and $\hat{b}=\hat{j}$ are such that $\vec{a},\vec{c}$ and $\vec{b}$ form a right handed system then $\vec{c}$ is :

   1. A.$z\hat{i}-x\hat{k}$
   2. B.$\vec{0}$
   3. C.$y\hat{j}$
   4. D.$-z\hat{i}+x\hat{k}$
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   Answer: A

5. Q412002 · 27 Apr 2002 · Shift 1

   $\vec{a}=3\hat{i}-5\hat{j}$ and $\vec{b}=6\hat{i}+3\hat{j}$ are two vectors and $\vec{c}$ is a vector such that $\vec{c}=\vec{a}\times \vec{b}$ then $|\vec{a}|:|\vec{b}|:|\vec{c}|=$

   1. A.$\sqrt{34}:\sqrt{45}:\sqrt{39}$
   2. B.$\sqrt{34}:\sqrt{45}:39$
   3. C.$34:39:45$
   4. D.$39:35:34$
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   Answer: B

6. Q682002 · 27 Apr 2002 · Shift 1

   If $\vec{a},\vec{b},\vec{c}$ are vectors such that $[\vec{a}\vec{b}\vec{c}]=4$ then $[\vec{a}\times \vec{b}\vec{b}\times \vec{c}\vec{c}\times \vec{a}]=$

   1. A.$16$
   2. B.$64$
   3. C.$4$
   4. D.$8$
   Show answer

   Answer: A