Vector Algebra · JEE Main previous year questions

2012 6 questions

1. Q202012 · 26 May 2012 · Shift 1

   The distance of the point $-\hat{i}+2\hat{j}+6\hat{k}$ from the straight line that passes through the point $2\hat{i}+3\hat{j}-4\hat{k}$ and is parallel to the vector $6\hat{i}+3\hat{j}-4\hat{k}$ is

   1. A.9
   2. B.8
   3. C.7
   4. D.10
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   Answer: C

2. Q282012 · 26 May 2012 · Shift 1

   Statement 1: The vectors $\vec{a},\vec{b}$ and $\vec{c}$ lie in the same plane if and only if $\vec{a}\cdot (\vec{b}\times \vec{c})=0$ Statement 2: The vectors $\vec{u}$ and $\vec{v}$ are perpendicular if and only if $\vec{u}\cdot \vec{v}=0$ where $\vec{u}\times \vec{v}$ is a vector perpendicular to the plane of $\vec{u}$ and $\vec{v}$

   1. A.Statement 1 is false, Statement 2 is true.
   2. B.Statement 1 is true, Statement 2 is true, Statement 2 is correct explanation for Statement 1.
   3. C.Statement 1 is true, Statement 2 is false.
   4. D.Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.
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   Answer: B

3. Q282012 · 12 May 2012 · Shift 1

   If $\vec{u}=\hat{j}+4\hat{k},\vec{v}=\hat{i}+3\hat{k}$ and $\vec{w}=\cos \theta \hat{i}+\sin \theta \hat{j}$ are vectors in 3-dimensional space, then the maximum possible value of $|\vec{u}\times \vec{v}\cdot \vec{w}|$ is

   1. A.$\sqrt{3}$
   2. B.5
   3. C.$\sqrt{14}$
   4. D.7
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   Answer: B

4. Q302012 · 12 May 2012 · Shift 1

   A unit vector which is perpendicular to the vector $2\hat{i}-\hat{j}+2\hat{k}$ and is coplanar with the vectors $\hat{i}+\hat{j}-\hat{k}$ and $2\hat{i}+2\hat{j}-\hat{k}$ is

   1. A.$\frac{2\hat{j}+\hat{k}}{\sqrt{5}}$
   2. B.$\frac{3\hat{i}+2\hat{j}-2\hat{k}}{\sqrt{17}}$
   3. C.$\frac{3\hat{i}+2\hat{j}+2\hat{k}}{\sqrt{17}}$
   4. D.$\frac{2\hat{i}+2\hat{j}-\hat{k}}{3}$
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   Answer: D

5. Q212012 · 7 May 2012 · Shift 1

   $ABCD$ is parallelogram. The position vectors of $A$ and $C$ are respectively, $3\hat{i}+3\hat{j}+5\hat{k}$ and $\hat{i}-5\hat{j}-5\hat{k}$. If $M$ is the midpoint of the diagonal $DB$, then the magnitude of the projection of $\overrightarrow{OM}$ on $\overrightarrow{OC}$, where $O$ is the origin, is

   1. A.$7\sqrt{51}$
   2. B.$\frac{7}{\sqrt{50}}$
   3. C.$7\sqrt{50}$
   4. D.$\frac{7}{\sqrt{51}}$
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   Answer: D

6. Q282012 · 7 May 2012 · Shift 1

   If $\vec{a}=\hat{i}-2\hat{j}+3\hat{k}$, $\vec{b}=2\hat{i}+3\hat{j}-\hat{k}$ and $\vec{c}=\lambda \hat{i}+\hat{j}+(2\lambda -1)\hat{k}$ are coplanar vectors, then $\lambda$ is equal to

   1. A.0
   2. B.$-1$
   3. C.2
   4. D.1
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   Answer: A