Vector Algebra · JEE Main previous year questions

2010 2 questions

1. Q212010 · 25 Apr 2010 · Shift 1

   If the vectors $\vec{a}=\hat{i}-\hat{j}+2\hat{k}$, $\vec{b}=2\hat{i}+4\hat{j}+\hat{k}$ and $\vec{c}=\lambda \hat{i}+\hat{j}+\mu \hat{k}$ are mutually orthogonal, then $(\lambda ,\mu )$ is equal to :

   1. A.$(2,-3)$
   2. B.$(-2,3)$
   3. C.$(3,-2)$
   4. D.$(-3,2)$
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   Answer: D

2. Q292010 · 25 Apr 2010 · Shift 1

   Let $\vec{a}=\hat{j}-\hat{k}$ and $\vec{c}=\hat{i}-\hat{j}-\hat{k}$. Then the vector $\vec{b}$ satisfying $\vec{a}\times \vec{b}+\vec{c}=\vec{0}$ and $\vec{a}\cdot \vec{b}=3$ :

   1. A.$2\hat{i}-\hat{j}+2\hat{k}$
   2. B.$\hat{i}-\hat{j}-2\hat{k}$
   3. C.$\hat{i}+\hat{j}-2\hat{k}$
   4. D.$-\hat{i}+\hat{j}-2\hat{k}$
   Show answer

   Answer: D