2. Let A, B, C and D be consecutive points of a parallelogram. Point E divides the diagonal AC so that |AE| |EC| = 1:3. Point F divides the diagonal BD so that |BD| : |BF| = 4: 3. Let S be the point of intersection of line segments AF and ED. (a) Write the vector AS as a linear combination of vectors = AC and 7 = BĎ. Hint: |AS| = |AF|. (b) If A(1, -2, 2), B(3,-1,4) and C(2, 3,-3), find the angle between line segments AB and BC and determine the area of the parallelogram. Hint: The angle between two vectors can be obtained from the equation cos y = |01|-|0₂|| √₁-√₂

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