A and b are two given vectors on these vectors as adjoint sides a parrallelogram is constructed. The vector which is the altitude of the parallelogram and which is perpendicular to a is
Answers
Answer:
the cross product
Step-by-step explanation:
There are two ways to take the product of a pair of vectors. One of these methods of multiplication is the cross product, which is the subject of this page. The other multiplication is the dot product, which we discuss on another page.
The cross product is defined only for three-dimensional vectors. If a and b are two three-dimensional vectors, then their cross product, written as a×b and pronounced “a cross b,” is another three-dimensional vector. We define this cross product vector a×b by the following three requirements:
a×b is a vector that is perpendicular to both a and b.
The magnitude (or length) of the vector a×b, written as ∥a×b∥, is the area of the parallelogram spanned by a and b (i.e. the parallelogram whose adjacent sides are the vectors a and b, as shown in below figure).
The direction of a×b is determined by the right-hand rule. (This means that if we curl the fingers of the right hand from a to b, then the thumb points in the direction of a×b.)
The below figure illustrates how, using trigonometry, we can calculate that the area of the parallelogram spanned by a and b is