1. Let ABCD be a square. The point M is chosen on the side AB so...

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1. Let ABCD be a square. The point M is chosen on the side AB so that |AM|:|MB| = 2 1. The point N is chosen on the side CD so that |CN| |ND| = 5 : 1. Find the measure of ZMNA. Use vectors in your solution. 2. In a trapezoid with vertices A(-3,-1), B(-2, 2), C(1, a), D(b, -3), the angle A is 90°. Find the numbers a, b and the measure of the angle C. Use vectors to solve the problem. 3. Show that the vectors u = (1, 0, 2), v = (-2,5, 1), and w = (2, 1, -1) span a paral- lelepiped. Is this parallelepiped rectangular? Justify your answer. Find the volume of the parallelepiped. 4. A parallelogram is spanned by the vectors (1, 3, 1) and (3, 1, 2). Find the angle between the diagonals of the parallelogram and the area of the parallelogram. 5. Do the points (2, 1,-2), (0, 3, 1), (4, 1,0) and (-2,-1,0) belong to the same plane? Justify your answer. 1. Let ABCD be a square. The point M is chosen on the side AB so that |AM|:|MB| = 2 1. The point N is chosen on the side CD so that |CN| |ND| = 5 : 1. Find the measure of ZMNA. Use vectors in your solution. 2. In a trapezoid with vertices A(-3,-1), B(-2, 2), C(1, a), D(b, -3), the angle A is 90°. Find the numbers a, b and the measure of the angle C. Use vectors to solve the problem. 3. Show that the vectors u = (1, 0, 2), v = (-2,5, 1), and w = (2, 1, -1) span a paral- lelepiped. Is this parallelepiped rectangular? Justify your answer. Find the volume of the parallelepiped. 4. A parallelogram is spanned by the vectors (1, 3, 1) and (3, 1, 2). Find the angle between the diagonals of the parallelogram and the area of the parallelogram. 5. Do the points (2, 1,-2), (0, 3, 1), (4, 1,0) and (-2,-1,0) belong to the same plane? Justify your answer.

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1 Lets denote the vectors AM and CN as vectors u and v respectively Since the square ABCD is a regular square the sides AB and CD are parallel Therefore vectors u and v are parallel as well Lets assum... View the full answer