Maths questions on dot product, vectors?

[latkan]

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

 

[rock.freak667]

to get the dot product, multiply the corresponding components and then add up all.

 

[Cyosis]

The dot product for vectors is defined as $$\vec{a} \cdot \vec{b}=a_1b_1+a_2 b_2+\ldots a_n b_n=||\vec{a}||||\vec{b}|| \cos \theta$$. What does it mean when two vectors are perpendicular to each other?