1 (a) Let A (0,2, 3), B ( 3,1,2), C (0,3,2), and D (3,4, 3) Show that ABCD is a parallelogram (ii) Let P be the midpoint of the line segment AC Find the vector OP (iii) Find the vectors B and P and deduce that the diagonals AC and BD bisect each other (iv) Find the lengths of A and B and deduce whether ABCD is a rectangle

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Question: 1. (a) Let A = (0,2, -3), B = (-3,1,2), C = (0,3,2), and D = (3,4, 3). Show that ABCD is a parallelogram.

1. (a) Let A = (0,2, -3), B = (-3,1,2), C = (0,3,2), and D = (3,4, – 3). Show that ABCD is a parallelogram. (ii) Let P be the midpoint of the line segment AC. Find the vector OP. (iii) Find the vectors BỊ and PĎ and deduce that the diagonals AC and BD bisect each other. (iv) Find the lengths of AČ and BỊ and deduce whether ABCD is a rectangle.

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