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## Homework Statement

1.

(a) Define carefully the dot and vector products of two vectors a and b.

(b) Show, using the dot product, that if c - d and c + d are perpendicular then |c| = |d|.

(c) The vectors a = i+2j and b = i - 2j + k form two sides of a triangle. Use vector methods to find the area of the triangle and the angle between a and b.3.

(a) Define carefully the dot and vector products of two vectors a and b.

(b) Two unit vectors c and d are perpendicular. Find (c x d) . (2c + 3d).

(c) The three points. (-1, 2, 2), (2, 0, 1) and (1,2,1) form the vertices of a triangle. Use vector methods to find the angle between the two sides of the triangle which meet at (1, 2, 1). Find, also, using vector methods, the area of the triangle.

4.

(a) Define the dot and the cross product between two vectors a and b.

(b) Two unit vectors c and d are perpendicular. Find (c x d) x c.

(c) The three points (1, -2, 1), (0, 2, 1) and (-1, 1, 2) form the vertices of a triangle. Use vector methods to find the angle between the two sides of the triangle which meet at (0, 2, 1). Find, also, using vector methods, the area of the triangle.

## Homework Equations

## The Attempt at a Solution

Stumped but i remember being told about x,y,z and a method of cross multiplying but other than that i dnt really know