Question

If the position vectors of the plane $A,B,C$ be $\hat{i}+\hat{j},\hat{i}-\hat{j}$ and $a\hat{i}+b\hat{j}+c\hat{k}$ respectively, then the points $A,B,C$ are collinear if

• A. $a=b=c=1$
• B. $a=1,b$ and $c$ are arbitrary scalars
• C. $a=b=c=0$
• D. $c=0,a=1$ and $b$ are arbitrary scalars

Answer 1

The correct option is D $c=0,a=1$ and $b$ are arbitrary scalars

A,B,C are collinear

$\therefore \Delta =\left[\begin{array}{ccc}1& 1& 0\\ 1& -1& 0\\ a& b& c\end{array}\right]=0\Rightarrow C(-1-1)=0\Rightarrow 2C=0\Rightarrow C=0$

$\therefore C=0,a=1$ and b has any arbitrary value.