I know you can use the cross product of two vectors (in 3 dimensions) to find th
ID: 2875027 • Letter: I
Question
I know you can use the cross product of two vectors (in 3 dimensions) to find the area of a parallelogram determined by them. What I'm wondering is why can't you just use a [Area=base * height] method (using the lengths of the vectors as base and height)?
For example, if we have a vector a and b in 3 dimensions, couldn't you find the area of a parallelogram determined by them by doing Area = (Length of a) * (length of b)?
I get conflicting answers on each random example I try, and I'm not sure why.
Thank you in advance!
Explanation / Answer
The only way is to use the cross product of two vectors to find the area of the parallelogram while the Two vectors are given.
The formula Area=base*height can not be used because , this formula is used only in two dimension.
But the area required is of Three-dimensional and hence we need something which involve all the three dimensions.
Hence we need cross Product.