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In the first question of this problem, we are given that a triangle has vertices a with coordinate 524, b with coordinates 336 and c with coordinates 773.
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We are asked to determine the area of this triangle, triangle a, b, c.
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Now, if a triangle has vertices a, b and c, then the area can be determined as half times the magnitude of the cross product of the vectors a, b and a .c.
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So here we need to first find the vector, vector a .b.
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Now vector a .b has components formed by subtracting the corresponding components of a, from the components of b.
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Therefore it has components 3 minus 5, 3 minus 2, 6 minus 4.
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Therefore vector ab is the vector with components negative 2 1 2.
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Similarly find the vector vector ac which is the vector with components 7 minus 5, 7 minus 2 and 3 minus 4.
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Therefore vector ac has components 2 5 negative 1 now find the cross product ab cross ac it is the determinant of the first draw is formed by the unit vectors i j and k the second row is formed by the components of vector ab which is negative to 1 2 and the last row is formed by the components of vector ac which are 2 5 negative 1 2...