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Three Dimensional Geometry — Maths STD 12 Science — Question

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

Answer

  1. Non collinear

Solution:

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 R2​ → R2​ − R1​, R3​ → R3 ​− 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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