Vector Algebra · JEE Main previous year questions

2004 4 questions

1. Q392004 · 24 Apr 2004 · Shift 1

   Let $\vec{a},\vec{b}$ and $\vec{c}$ be three non-zero vectors such that no two of these are collinear. If the vector $\vec{a}+2\vec{b}$ is collinear with $\vec{c}$ and $\vec{b}+3\vec{c}$ is collinear with $\vec{a}$ ($\lambda$ being some non-zero scalar) then $\vec{a}+2\vec{b}+6\vec{c}$ equals to :

   1. A.$\vec{0}$
   2. B.$\lambda \vec{b}$
   3. C.$\lambda \vec{c}$
   4. D.$\lambda \vec{a}$
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   Answer: A

2. Q402004 · 24 Apr 2004 · Shift 1

   Let $\vec{u},\vec{v},\vec{w}$ be such that $|\vec{u}|=1,|\vec{v}|=2,|\vec{w}|=3$. If the projection of $\vec{v}$ along $\vec{u}$ is equal to that of $\vec{w}$ along $\vec{u}$ and $\vec{v},\vec{w}$ are perpendicular to each other then $|\vec{u}-\vec{v}+\vec{w}|$ equals :

   1. A.$14$
   2. B.$\sqrt{7}$
   3. C.$\sqrt{14}$
   4. D.$2$
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   Answer: C

3. Q412004 · 24 Apr 2004 · Shift 1

   Let $\vec{a},\vec{b}$ and $\vec{c}$ be non-zero vectors such that $(\vec{a}\times \vec{b})\times \vec{c}=\frac{1}{3}|\vec{b}||\vec{c}|\vec{a}$. If $\theta$ is the acute angle between the vectors $\vec{b}$ and $\vec{c}$, then $\sin \theta$ equals :

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

4. Q682004 · 24 Apr 2004 · Shift 1

   If $\vec{a},\vec{b},\vec{c}$ are non-coplanar vectors and $\lambda$ is a real number, then the vectors $\vec{a}+2\vec{b}+3\vec{c},\lambda \vec{b}+4\vec{c}$ and $(2\lambda -1)\vec{c}$ are non coplanar for :

   1. A.no value of $\lambda$
   2. B.all except one value of $\lambda$
   3. C.all except two values of $\lambda$
   4. D.all values of $\lambda$
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   Answer: C