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10. vector algebra — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths10. vector algebra1 Mark
MCQ
The value of $\lambda $ for which points $A(2,2,1)$ , $B(1,1,1)$ , $C(-\lambda ,2,1)$ and $D(3,0,-1)$ are coplanar, is $\lambda  =$  ............ 
  • ✓
    $-2$
  • B
    $1$
  • C
    $2$
  • D
    $-1$
✓

Answer

Correct option: A.
$-2$
a
$[\overrightarrow {{\rm{AB}}} \,\overrightarrow {{\rm{AC}}} \,\overrightarrow {{\rm{AD}}} ] = 0$

$\Rightarrow\left|\begin{array}{ccc}{-1} & {-1} & {0} \\ {-\lambda-2} & {0} & {0} \\ {1} & {-2} & {-2}\end{array}\right|=0 \Rightarrow \lambda=-2$

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