Vector Algebra · JEE Main previous year questions

2006 2 questions

1. Q292006 · 29 Apr 2006 · Shift 1

   The values of a, for which the points $A,B,C$ with position vectors $2\hat{i}-\hat{j}+\hat{k}$, $\hat{i}-3\hat{j}-5\hat{k}$ and $a\hat{i}-3\hat{j}+\hat{k}$ respectively are the vertices of a right angled triangle with $C=\frac{\pi }{2}$ are :

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

2. Q392006 · 29 Apr 2006 · Shift 1

   If $(\vec{a}\times \vec{b})\times \vec{c}=\vec{a}\times (\vec{b}\times \vec{c})$ where $\vec{a},\vec{b}$ and $\vec{c}$ are any three vectors such that $\vec{a}\cdot \vec{b}\ne 0$, $\vec{b}\cdot \vec{c}\ne 0$ then $\vec{a}$ and $\vec{c}$ are :

   1. A.inclined at an angle of $\frac{\pi }{3}$ between them
   2. B.inclined at an angle of $\frac{\pi }{6}$ between them
   3. C.perpendicular
   4. D.parallel
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   Answer: D