Vectors · NDA previous year questions

2009 15 questions

1. Q1002009 · 19 Apr 2009

   Let $\vec{a},\vec{b},\vec{c}$ be the position vectors of points $A,B,C$ respectively. Under which one of the following conditions are the points $A,B,C$ collinear?

   1. A.$\vec{a}\times \vec{b}=\vec{0}$
   2. B.$\vec{b}\times \vec{c}$ is parallel to $\vec{a}\times \vec{b}$
   3. C.$\vec{a}\times \vec{b}$ is perpendicular to $\vec{b}\times \vec{c}$
   4. D.$(\vec{a}\times \vec{b})+(\vec{b}\times \vec{c})+(\vec{c}\times \vec{a})=\vec{0}$
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   Answer: D

2. Q1012009 · 19 Apr 2009

   If $\vec{a}=\hat{i}+\hat{j}+\hat{k},\vec{b}=\hat{i}-\hat{j}+\hat{k}$ and $\vec{c}=\hat{i}+\hat{j}-\hat{k}$, then what is $\vec{a}\times (\vec{b}+\vec{c})+\vec{b}\times (\vec{c}+\vec{a})+\vec{c}\times (\vec{a}+\vec{b})$ equal to?

   1. A.$2\hat{i}+3\hat{j}-\hat{k}$
   2. B.$2\hat{i}-3\hat{j}-\hat{k}$
   3. C.$3\hat{i}+\hat{j}+\hat{k}$
   4. D.$\vec{0}$
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   Answer: D