The direction ratios of the two lines $A B$ and $A C$ are $1,-1,-1$ and $2,-1,1$. The direction ratios of…

The direction ratios of the two lines $A B$ and $A C$ are $1,-1,-1$ and $2,-1,1$. The direction ratios of the normal to the plane $A B C$ are
  1. $2,3,-1$
  2. $2,2,1$
  3. $3,2,-1$
  4. $-1,2,3$

Solution

Direction ratios of $A B$ and $A C$ are $\langle 1,-1,-1\rangle$ and $ < 2,-1,1\rangle$, respectively.
$ \left.\begin{array}{ll} \therefore & x_2-x_1=1 \\ & y_2-y_1=-1 \\ & z_2-z_1=-1 \end{array}\right\} $ From Eqs. (i) and (ii), $ \left.\begin{array}{l} x_2-x_3=3 \quad \Rightarrow x_3-x_2=-3 \\ y_2-y_3=-2 \quad \Rightarrow y_3-y_2=2 \\ z_2-z_3=0 \quad \Rightarrow z_3-z_2=0 \end{array}\right\} $

Asked in: AP EAMCET 2013

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