MCQ
The points $A(4,\,5,\,1),B(0, - 1, - 1),C(3,\,9,\,4)$ and $D( - 4,\,4,\,4)$ are
- ACollinear
- ✓Coplanar
- CNon- coplanar
- DNon- Collinear and non-coplanar
$AC \equiv ( - 1,\,4,\,3)$;
$AD \equiv ( - 8,\, - 1,\,3)$
Points $A, B, C, D$ are coplaner,
if $[\overrightarrow {AB} ,\,\overrightarrow {AC} ,\,\overrightarrow {AD} ] = 0$
==> $\left| {\,\begin{array}{*{20}{c}}{ - 4}&{ - 6}&{ - 2}\\{ - 1}&4&3\\{ - 8}&{ - 1}&3\end{array}\,} \right|\, = \,0$.
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
| $\text{X}:$ | $2$ | $3$ | $4$ | $5$ |
| $\text{P}(\text{X}):$ | $\frac{5}{\text{k}}$ | $\frac{7}{\text{k}}$ | $\frac{9}{\text{k}}$ | $\frac{11}{\text{k}}$ |
Statement $-1 :$ $f\left( c \right) = \frac{1}{3}$ for some $c\; \in R$
Statement $-2 :$$0 < f\left( x \right) < \frac{1}{{2\sqrt 2 }}\;,\forall x\; \in R$