Question

$A,B,C$ are three vectors given by $2i+k,i+j+k$ and $4i-3j+7k$. Then, find $R$ which satisfies the relation $R\times B=C\times B$ and $R\cdot A=0$.

• A. $R=i-16j-2k$
• B. $R=-i-8j+2k$
• C. $R=-2i+8j+2k$
• D. $R=i+8j+4k$

Answer 1

Answer: (B)

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

Given $A=2i+k$ , $B=i+j+k$ and $C=4i-3j+7k$

Let $R$ be $xi+yj+zk$

Given $R.A=0$

$\Rightarrow 2x+z=0$

Given $(R-C)\times B=0$

$\Rightarrow \left(\right(x-4)i+(y+3)j+(z-7\left)k\right)\times (i+j+k)=0$

$\Rightarrow (y-z+10)i-(x-z+3)j+(x-y-7)k=0$

$\Rightarrow z-y=10,z-x=3,x-y=7$

By solving above three equations , we get $x=-1,y=-8,z=2$

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