Vector Algebra · JEE Main previous year questions

2005 2 questions

1. Q422005 · 28 Apr 2005 · Shift 1

   For any vector $\vec{a}$, the value of ${\left(\vec{a}\times \hat{i}\right)}^2+{\left(\vec{a}\times \hat{j}\right)}^2+{\left(\vec{a}\times \hat{k}\right)}^2$ is equal to :

   1. A.$3{\vec{a}}^2$
   2. B.${\vec{a}}^2$
   3. C.$2{\vec{a}}^2$
   4. D.$4{\vec{a}}^2$
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   Answer: C

2. Q702005 · 28 Apr 2005 · Shift 1

   If $\vec{a},\vec{b},\vec{c}$ are non coplanar vectors and $\lambda$ is a real number then $$\left[\lambda \left(\vec{a}+\vec{b}\right){\lambda }^2\vec{b}\lambda \vec{c}\right]=\left[\vec{a}\vec{b}+\vec{c}\vec{b}\right]\text{ for :}$$

   1. A.exactly one value of $\lambda$
   2. B.no value of $\lambda$
   3. C.exactly three values of $\lambda$
   4. D.exactly two values of $\lambda$
   Show answer

   Answer: B