Calc_Lecture_06

Calc_Lecture_06 - Distances Between Points, Planes, and...

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1 Distances Between Points, Planes, and Lines

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2 This section is concluded with the following discussion of two basic types of problems involving distance in space. 1. Finding the distance between a point and a plane 2. Finding the distance between a point and a line The distance D between a point Q and a plane is the length of the shortest line segment connecting Q to the plane, as shown in Figure 11.52. Figure 11.52 Distances Between Points, Planes, and Lines
3 Distances Between Points, Planes, and Lines If P is any point in the plane, you can find this distance by projecting the vector onto the normal vector n . The length of this projection is the desired distance.

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4 Example 5 – Finding the Distance Between a Point and a Plane Find the distance between the point Q (1, 5, –4 ) and the plane given by 3 x y + 2 z = 6. Solution: You know that is normal to the given plane. To find a point in the plane, let y = 0 and z = 0 and obtain the point P (2, 0, 0). The vector from P to Q is given by
5 Example 5 – Solutions Using the Distance Formula given in Theorem 11.13 produces cont’d

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This note was uploaded on 10/05/2011 for the course BIO 203, CH taught by Professor Lacey,simmerling,deng,hanson during the Fall '10 term at SUNY Stony Brook.

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Calc_Lecture_06 - Distances Between Points, Planes, and...

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