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Vectors — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsVectors2 Marks
MCQ
If $3 \bar{P}+2 \bar{R}-5 \bar{Q}=\overline{0}$, then
  • ✓
    $P, Q, R$ are collinear
  • B
    $P, Q, R$ vertices of a $\Delta$
  • C
    Q divides PR externally
  • D
    none of these
✓

Answer

Correct option: A.
$P, Q, R$ are collinear
(A) $3 \overline{ P }+2 \overline{ R }-5 \overline{ Q }=\overline{0}$
$\Rightarrow 3 \overline{ P }+2 \overline{ R }=5 \overline{ Q }$
$\Rightarrow \overline{ Q }=\frac{3 \overline{ P }+2 \overline{ R }}{5}$
$\overline{ Q }$ is the position vector of the point dividing $P$ and $R$ in the ratio $3: 2$ internally. Thus, $P , Q$ and R are collinear.

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