For example, given the vector AB = (2, 3) and the vector SD (5, 8), find the vector AB × vector SD =? Vector AB×Vector SD=2×5+3×8=34
There are two types of vector multiplication, fractional product and vector product:
向量 a = (x, y, z),
Vector b = (u, v, w),
Quantity product (dot product): a·b = xu+yv+zw
Vector product (cross product): a×b =
|i j k|
|x y z|
|u v w|
The notation of vectors: the printed letters are marked as bold letters (such as a, b, u, v), and a small arrow "→" is added to the top of the letter when writing. If the start point (A) and end point (B) of a vector are given, the vector can be recorded as AB (and add → on top). In the spatial rectangular coordinate system, vectors can also be expressed in pairs. For example, (2,3) in the xOy plane is a vector.
Extended information:
Generally, printing is represented by bold lowercase English letters (a, b, c, etc.), and handwriting is represented by adding an arrow (→) to letters such as a, b, c, etc., for example, capital letters AB, CD can also be added An arrow (→) etc. means, for example,.
In a rectangular coordinate system, two unit vectors i and j in the same direction as the x-axis and y-axis are taken as a set of bases.
It is an arbitrary vector in the plane rectangular coordinate system, and the vector is taken as the starting point of the coordinate origin O.
From the fundamental theorem of plane vectors, we know that there is one and only one pair of real numbers (x, y), so that, therefore, the real number pairs are called the coordinates of the vector and denoted by. This is the coordinate representation of the vector. Among them are the coordinates of the point. The vector is called the position vector of the point P.
Non-zero vectors with the same or opposite directions are called parallel (or collinear) vectors. The vectors a and b are parallel (collinear), denoted as a∥b. The length of the zero vector is zero, which is a vector whose start point and end point coincide, and its direction is uncertain. We stipulate that the zero vector is parallel to any vector. A group of vectors parallel to the same straight line are collinear vectors.
If a=(x,y), b=(m,n), then a//b→a×b=xn-ym=0