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Three Dimensional Geometry — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSThree Dimensional Geometry1 Mark
MCQ
Are the points $(1, 1), (2, 3)$ and $(8, 11)$ collinear?
  • A
    collinear
  • ✓
    Non collinear
  • C
    coplaner
  • D
    None of above
✓

Answer

Correct option: B.
Non collinear
Area of triangle formed by these vertices is,
$\triangle=\frac{1}{2}\begin{vmatrix}1&1&1\\2&3&1\\8&11&1\end{vmatrix}$
Applying $R_2​ \rightarrow R_2​ − R_1​, R_{3​ }\rightarrow R_{3 ​}− R1​$
$\triangle=\frac{1}{2}\begin{vmatrix}1&1&1\\1&2&0\\7&10&0\end{vmatrix}=\frac{1}{2}(10-14)=2$
Hence points are non collinear

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