***Question 6 for reference - please answer Question 8 ****

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Question 6:

We assume given a plane U passing by the tip of the vectors ~u =< -1, 1, 2 >, ~v =< 2, -1, 0 > and w~ =< 1, 1, 3 >.

(6.1) Find the dot products ~u ~v and w~ ~v

(6.2) Determine whether or not there is a vector ~n that is perpendicular to U. If yes, then find the vector ~n. Otherwise explain why such a vector does not exist?

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Question 8: 17 Marks

Compute and find a relation between the expressions

(8.1) ~u (~v w~ ), w~ (~u ~v), and ~v (w~ ~u)

Find an expression for

(8.2) ~u (~v w~ ) and ~u (~v w~ )

(8.3) Find the side lengths and angles of the triangle with vertices the tips the vectors in Question

6 above.

(8.4) Use ~u and ~v from Question 6 to find the area of the parallelogram formed by ~u and ~v.

(8.5) Use ~u, ~v and w~ from Question 6 to find the volume of the parallelepiped with edges deter-

mined by the three vectors ~u, ~v and w~ .