Question

Assertion :Four points $A(3,-2,-1),B(2,3,-4),C(-1,1,2)$ and $D(4,5,\lambda )$ are coplanar for $\lambda =\frac{-17}{146}.$ Reason: Four points $A,B,C,D$ are coplanar then $\left[\overline{AB}\overline{AC}\overline{AD}\right]=0.$

• A. Both Assertion & Reason are individually true & Reason is correct explanation of Assertion,
• B. Both Assertion & Reason are individually true but Reason is not the correct explanation of Assertion
• C. Assertion is true but Reason is false
• D. Assertion is false but Reason is true

Answer 1

The correct option is D Assertion is false but Reason is true

The, points $A,B,C,D$ will be coplanar

$\Rightarrow \left[\overline{AB}\overline{AC}\overline{AD}\right]=0$

$\Rightarrow \left|\begin{array}{ccc}-1& 5& -3\\ -4& 3& 3\\ 1& 7& \lambda +1\end{array}\right|=0$

$\Rightarrow 146+17\lambda =0$

$\Rightarrow \lambda =\frac{-146}{17}$

So, Assertion is false.