12.3 plane vector coordinate representation: 1. The coordinate representation of the plane vector 1. In the plane rectangular coordinate system , let the two unit vectors that are the same as the x-axis and y-axis directions are i, j, and {i, j} are taken as the base. For any vector a in the plane, it can be seen from the basic theorem of plane vector that there are only one pair of real numbers x, y, so that a=xi+yj. Any vector a in the plane can be uniquely determined by x and y. We call the ordered pair (x, y) the coordinates of vector a, and denoted as a=(x, y).2. In the rectangular coordinate plane, i=(1,0), j=(0,1), 0=(0,0). [Thinking] What is the difference and connection between the coordinates of points and the vector coordinates?
2. Coordinate operation of plane vector: 1. The coordinates of plane vector addition and subtraction operations represent
Known points A(x1, y1), B(x2, y2), then vector = (x2-x1, y2-y1), that is, the coordinates of any vector are equal to the coordinates representing the end point of the directed line segment of this vector minus the coordinates of the starting point.
3, plane vector quantity product ht The coordinates of ml2 are indicated. Let the non-zero vector a=(x1, y1), b=(x2, y2), and the angle between a and b is θ. Then a·b=x1x2+y1y2.
If the coordinates of the starting point and end point of the directed line segment of vector a are (x1, y1), (x2, y2),
2.a⊥b⇔x1x2+y1y2=0.3.
[Thinking] If the angle between two non-zero vectors satisfies cos θ0, then is the angle θ of the two vectors necessarily an obtuse angle? [Answer] Not necessarily. When cos θ0, the angle θ of the two vectors may be an obtuse angle, or it may be 180°.
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