The points A(4, ,5, ,1),B(0, - 1, - 1),C(3, ,9, ,4) and D( - 4, ,… - Vidyadip

MCQ

The points $A(4,\,5,\,1),B(0, - 1, - 1),C(3,\,9,\,4)$ and $D( - 4,\,4,\,4)$ are

A
Collinear
✓
Coplanar
C
Non- coplanar
D
Non- Collinear and non-coplanar

✓

Answer

Correct option: B.

Coplanar

b
(b) $AB \equiv ( - 4,\, - 6,\, - 2);$

$AC \equiv ( - 1,\,4,\,3)$;

$AD \equiv ( - 8,\, - 1,\,3)$

Points $A, B, C, D$ are coplaner,

if $[\overrightarrow {AB} ,\,\overrightarrow {AC} ,\,\overrightarrow {AD} ] = 0$

==> $\left| {\,\begin{array}{*{20}{c}}{ - 4}&{ - 6}&{ - 2}\\{ - 1}&4&3\\{ - 8}&{ - 1}&3\end{array}\,} \right|\, = \,0$.

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