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VECTORS APPLICATIONS NHAA/IMK/UNIMAP.

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Presentation on theme: "VECTORS APPLICATIONS NHAA/IMK/UNIMAP."— Presentation transcript:

1 VECTORS APPLICATIONS NHAA/IMK/UNIMAP

2 APPLICATIONS Lines & Line Segment in Space Parametric Equations z L v
y x P0(x0,y0,z0) L P(x,y,z) v Line L is the set of all points P(x,y,z) for which parallel to NHAA/IMK/UNIMAP

3 APPLICATIONS Therefore the parametric equation for L : Cartesian equation: Parametric Equation NHAA/IMK/UNIMAP

4 Example 1 Find parametric and Cartesian equation for the line passes through Q(-2,0,4) and parallel to NHAA/IMK/UNIMAP

5 Example 2 Find the parametric equation for the line passes through P(-3,2,-3) and Q(1,-1,4)
NHAA/IMK/UNIMAP

6 APPLICATIONS Distance from point S to line L L
v L From the properties of Cross Product Formula of Distance from point S to L NHAA/IMK/UNIMAP

7 Example 3 Find the distance from the point S(1,1,5) to the line
NHAA/IMK/UNIMAP

8 APPLICATIONS Equation of Planes
P0(x0,y0,z0) P(x,y,z) Vector is on the plane M and vector which is perpendicular to M known as normal vector, n Equation of Plane is defined by: From the properties of Dot Product NHAA/IMK/UNIMAP

9 APPLICATIONS Equation of Planes Normal vector n : NHAA/IMK/UNIMAP

10 APPLICATIONS Let and EQUATION OF PLANE NHAA/IMK/UNIMAP

11 Example 4 Find an equation of plane through P0(-3,0,7) perpendicular to
NHAA/IMK/UNIMAP

12 Example 7: Find equation of plane through 3 points:
NHAA/IMK/UNIMAP

13 APPLICATIONS Lines of Intersection 2 planes parallel if and only if their normal planes are parallel 2 planes that are not parallel, intersect in a line nM nN Normal vector for plane M and N v Line of intersection NHAA/IMK/UNIMAP

14 APPLICATIONS Lines of Intersection nM Finding v : nN v
Line of intersection NHAA/IMK/UNIMAP

15 Example 8: Find a vector parallel to the line of intersection of the planes
NHAA/IMK/UNIMAP

16 Example 9: Find the parametric equation for the line in which the planes intersect.
NHAA/IMK/UNIMAP

17 APPLICATIONS Distance from a Point to the Plane P n D P0
NHAA/IMK/UNIMAP

18 APPLICATIONS Equation of plane NHAA/IMK/UNIMAP

19 Example 10: Find the distance from S(1,1,3) to the plane
NHAA/IMK/UNIMAP

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