Given the plane P which contains the points A(3, 2,-4), B(5, 2, 1) and C(2, -3,-4)....

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Given the plane P which contains the points A(3, 2,-4), B(5, 2, 1) and C(2, -3,-4). Note: Write your answers in the vector form of ai + bj + ck. a) Find the position vector AB. AB= 2i+5k b) Find the position vector AC. AC = -i-5j c) Find AB X AC. AB x AC = 25i - 5j - 10k d) Determine the parametric equations for the line passing through point A and perpendicular to the plane P. Equations for the line: e) Find the area of the parallelogram containing the points A, B & C on the plane P. (Note: Round answer to 2 decimal places) Area = f) Determine the equation of the plane P through point A. (in the form of ax + by + cz + d = 0). plane P: Given the plane P which contains the points A(3, 2,-4), B(5, 2, 1) and C(2, -3,-4). Note: Write your answers in the vector form of ai + bj + ck. a) Find the position vector AB. AB= 2i+5k b) Find the position vector AC. AC = -i-5j c) Find AB X AC. AB x AC = 25i - 5j - 10k d) Determine the parametric equations for the line passing through point A and perpendicular to the plane P. Equations for the line: e) Find the area of the parallelogram containing the points A, B & C on the plane P. (Note: Round answer to 2 decimal places) Area = f) Determine the equation of the plane P through point A. (in the form of ax + by + cz + d = 0). plane P: