If x1 y1 1 x2 y2 1 x3 y3 1 - a1 b1 1 a2 b2 1 a3 b3 1 then the two triangles with vertices x1- y1- x2- y2- x3- y3 and a1- b1- a2- b2- a3- b3 are

The correct option is A equal in area. #160; x_1 amp; y_1 amp;1 x_2 amp; y_2 amp;1 x_3 amp; y_3 amp;1 #160;is a determinant which ...

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Multiplication with Vectors

If x1 y1 ...

Question

If $∣ ∣ ∣ ∣ \begin{matrix} x_{1} & y_{1} & 1 x_{2} & y_{2} & 1 x_{3} & y_{3} & 1 \end{matrix} ∣ ∣ ∣ ∣ = ∣ ∣ ∣ ∣ \begin{matrix} a_{1} & b_{1} & 1 a_{2} & b_{2} & 1 a_{3} & b_{3} & 1 \end{matrix} ∣ ∣ ∣ ∣$ then the two triangles with vertices $(x_{1}, y_{1}), (x_{2}, y_{2}), (x_{3}, y_{3})$ and $(a_{1}, b_{1}), (a_{2}, b_{2}), (a_{3}, b_{3})$ are

equal in area.

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similar.

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congruent.

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none of these.

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∣ ∣ ∣ ∣ \begin{matrix} x_{1} & y_{1} & 1 x_{2} & y_{2} & 1 x_{3} & y_{3} & 1 \end{matrix} ∣ ∣ ∣ ∣ = ∣ ∣ ∣ ∣ \begin{matrix} a_{1} & b_{1} & 1 a_{2} & b_{2} & 1 a_{3} & b_{3} & 1 \end{matrix} ∣ ∣ ∣ ∣

(x_{1}, y_{1}), (x_{2}, y_{2}), (x_{3}, y_{3})

(a_{1}, b_{1})

(a_{2}, b_{2})

(a_{3}, b_{3})

∣ ∣ ∣ ∣ \begin{matrix} x_{1} & y_{1} & 1 x_{2} & y_{2} & 1 x_{3} & y_{3} & 1 \end{matrix} ∣ ∣ ∣ ∣

∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 b_{1} & b_{2} & b_{3} a_{1} & a_{2} & a_{3} \end{matrix} ∣ ∣ ∣ ∣

(x_{1}, y_{1}), (x_{2}, y_{2}), (x_{3}, y_{3})

(a_{1}, b_{1}), (a_{2}, b_{2}), (a_{3}, b_{3})

∣ ∣ ∣ ∣ \begin{matrix} x_{1} & y_{1} & 1 x_{2} & y_{2} & 1 x_{3} & y_{3} & 1 \end{matrix} ∣ ∣ ∣ ∣ = ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 b_{1} & b_{2} & b_{3} a_{1} & a_{2} & a_{3} \end{matrix} ∣ ∣ ∣ ∣

(x_{1}, y_{1}), (x_{2}, y_{2}), ((x_{3}, y_{3})

(a_{1}, b_{1}), (a_{2}, b_{2}), (a_{13}, b_{3}),

∣ ∣ ∣ ∣ \begin{matrix} x_{1} & y_{1} & 1 x_{2} & y_{2} & 1 x_{3} & y_{3} & 1 \end{matrix} ∣ ∣ ∣ ∣ = ∣ ∣ ∣ ∣ \begin{matrix} a_{1} & b_{1} & 1 a_{2} & b_{2} & 1 a_{3} & b_{3} & 1 \end{matrix} ∣ ∣ ∣ ∣

(x_{1}, y_{1}), (x_{2}, y_{2}) (x_{3}, y_{3}) a n d (a_{1}, b_{1}), (a_{2}, b_{2}), (a_{3}, b_{3})

∣ ∣ ∣ ∣ \begin{matrix} x_{1} & y_{1} & 1 x_{2} & y_{2} & 1 x_{3} & y_{3} & 1 \end{matrix} ∣ ∣ ∣ ∣ = ∣ ∣ ∣ ∣ \begin{matrix} a_{1} & b_{1} & 1 a_{2} & b_{2} & 1 a_{3} & b_{3} & 1 \end{matrix} ∣ ∣ ∣ ∣

(x_{1}, y_{1}), (x_{2}, y_{2}), (x_{3}, y_{3})

(a_{1}, b_{1}), (a_{2}, b_{2}), (a_{3}, b_{3})

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