Question

If $A=2i+k,B=i+j+k$ and $C=4i-3j+7k$, then a vector $r$ which satisfies $R\times B=C\times B$ and $R.A=0$, is

• A. $-i-8j+2k$
• B. $i-8j+2k$
• C. $i+8j+2k$
• D. none of these

Answer 1

The correct option is A $-i-8j+2k$

Let $R=xi+yj+zk$

$\therefore R.A=0\Rightarrow 2x+z=0$ ....(1)

$R\times B=C\times B\Rightarrow \left|\begin{array}{ccc}i& j& k\\ x& y& z\\ 1& 1& 1\end{array}\right|=\left|\begin{array}{ccc}i& j& k\\ 4& -3& 7\\ 1& 1& 1\end{array}\right|\Rightarrow (y-z)i+(z-x)j+(x-y)k=-10i+3j+7k$

$\Rightarrow y-z=-10$ ...(2)

$z-x=3$ ...(3)

and $x-y=7$

Solving (1) and (2), we get $x=-1,z=2$

$\therefore$ From (2), $y=-8$

Hence $R=-i-8j+2k$