From the above it is clear that if two vectors are perpendicular, their dot product will be zero.
The cross-product, or vector-product as it is sometimes called, produces a vector that is perpendicular to the two vectors being crossed.
The area of a parallelogram spanned by two vectors , and it follows that the area of a triangle spanned by two vectors , because a triangle is half a parallelogram.
I think that's all the information you need to do these problems. Post again if you need more help.