Mathematics

Mathematics

Problem

Consider the points P(3,7)P(3,7), Q(−2,4)Q(-2,4) and R(5,−1)R(5,-1) taken in the order P, Q, RP,\,Q,\,R. What is the sign of the determinant ∣371−2415−11∣\begin{vmatrix}3 & 7 & 1\\ -2 & 4 & 1\\ 5 & -1 & 1\end{vmatrix} and hence the orientation of the triangle? a) Positive; vertices are clockwise b) Zero; vertices are collinear c) Positive; vertices are counter-clockwise d) Negative; vertices are clockwise

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