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rectangular cartensian co-ordinates — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSrectangular cartensian co-ordinates1 Mark
MCQ
The area of the triangle formed by the points $(a,b + c),\,(b,c + a),\,(c,a + b)$ is
  • A
    $abc$
  • B
    ${a^2} + {b^2} + {c^2}$
  • C
    $ab + bc + ca$
  • ✓
    $0$
✓

Answer

Correct option: D.
$0$
d
(d) Area$ = \frac{1}{2}\,\left| {\,\begin{array}{*{20}{c}}a&{b + c}&1\\b&{c + a}&1\\c&{a + b}&1\end{array}\,} \right| = \frac{1}{2}\,\left| {\,\begin{array}{*{20}{c}}a&{a + b + c}&1\\b&{a + b + c}&1\\c&{a + b + c}&1\end{array}\,} \right|$

(Applying ${C_2} \to {C_1} + {C_2})$

$ = \frac{{(a + b + c)}}{2}\,\left| {\,\begin{array}{*{20}{c}}a&1&1\\b&1&1\\c&1&1\end{array}\,} \right| = 0$.

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