lect10_2

lect10_2 - Vectors In The Space - (10.2) 1. A Right-handed...

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Vectors In The Space - (10.2) 1. A Right-handed Coordinate System We use a right-handed ! x , y , z " coordinate system. A point in the space can be represented by a , b , c where a , b , and c are real numbers. The system consists of three axes: x ! axis, y ! axis, and z ! axis, three planes: xy ! plane, yz ! plane, and xz ! plane, and eight octants. We can describe the planes and octants as follows: x ! axis: y ! 0, z ! 0 y ! axis: x ! 0, z ! 0 z ! axis: x ! 0, y ! 0 , xy ! plane: z ! 0 yz ! plane: x ! 0 xz ! plane: y ! 0 , first octants: x " 0, y " 0, and c " 0 Example Describe the plane which is parallel to xy ! plane and has a point ! ! 1,2,3 " . Since it is parallel to xy ! plane, a point ! a , b , c " on the plane has a constant c . Since the point ! ! 1,2,3 " is in the plane and c ! 3, the third component of every point is 3. So, the equation of this plane is: z ! 3. -4 -2 2 4 z -5 5 y 4 x z ! 3 2. Distance Between Two Points The distance between two points P ! x 1 , y 1 , z 1 " and Q ! x 2 , y
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lect10_2 - Vectors In The Space - (10.2) 1. A Right-handed...

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