Vector Algebra · JEE Main previous year questions

2009 2 questions

1. Q172009 · 27 Apr 2009 · Shift 1

   The projections of a vector on the three coordinate axis are $6,-3,2$ respectively. The direction cosines of the vector are :

   1. A.$\frac{6}{5},\frac{-3}{5},\frac{2}{5}$
   2. B.$\frac{6}{7},\frac{-3}{7},\frac{2}{7}$
   3. C.$\frac{-6}{7},\frac{-3}{7},\frac{2}{7}$
   4. D.$6,-3,2$
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   Answer: B

2. Q292009 · 27 Apr 2009 · Shift 1

   If $\vec{u},\vec{v},\vec{w}$ are non-coplanar vectors and $p,q$ are real numbers, then the equality $$\left[3\vec{u}p\vec{v}p\vec{w}\right]-\left[p\vec{v}\vec{w}q\vec{u}\right]-\left[2\vec{w}q\vec{v}q\vec{u}\right]=0$$ holds for :

   1. A.exactly two values of $(p,q)$
   2. B.more than two but not all values of $(p,q)$
   3. C.all values of $(p,q)$
   4. D.exactly one value of $(p,q)$
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   Answer: D