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5. a) Suppose that the area of the parallelogram spanned by the vectors ~u and ~v...

5. a) Suppose that the area of the parallelogram spanned by the vectors ~u and ~v is 10. What is the area of the parallogram spanned by the vectors 2~u + 3~v and −3~u + 4~v ?

(b) Given (~u × ~v) · ~w = 10. What is ((~u + ~v) × (~v + ~w)) · ( ~w + ~u)? [4]

6. Find an equation of the plane that is perpendicular to the plane x + 2y + 4 = 0, contains the origin, and whose normal makes an angle of 30◦ with the z − axis.

Please answer both questions with detailed solution.

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