Example:- Find a vector perpendicular to the plane of P(1,-1,0) and Q(2,1,-1) and R(-1,1,2)?
Solution:-
Example:- find unit normal vector perpendicular to the plane of T(2,-1,0) and P(3,1,-1) and K(1,1,1)?
Solution:-
Lines and Line Segments in Space
In the plane, a line is determined by a point and a number giving the slope of the line. In space a line is determined by a point and a vector giving the direction of the line. Suppose that L is a line in space passing through a point Po(xo, yo, zo) parallel to a vectorm v ? = Ai + Bj + Ck. Then L is the set of all points P(x, y, z) for which (PoP) ? is parallel to v ?.Thus,( (PoP) ? = t v ?) for some scalar parameter (t). The value of (t )depends on the location of the point P along the line, and the domain of ( t ) is ((?,?- The expanded form of the equation (PoP) ? = t( v) ? is
(PoP) ? =(x-x0)i+(y-y0)j+(z-z0)k = t (Ai + Bj + Ck)=tAi+tBj+tCk
The Distance from a Point to a Line in Space
To find the distance from point p to a line L , find the point Q on L closest to P and calculate the distance from P to Q
Example: Find the distance from the point P (1, 1,5) to the line L:
x = 1 + t, y = 3 - t, z = 2t.
Solution: find Q =(1+t,3-t,2t)
المادة المعروضة اعلاه هي مدخل الى المحاضرة المرفوعة بواسطة استاذ(ة) المادة . وقد تبدو لك غير متكاملة . حيث يضع استاذ المادة في بعض الاحيان فقط الجزء الاول من المحاضرة من اجل الاطلاع على ما ستقوم بتحميله لاحقا . في نظام التعليم الالكتروني نوفر هذه الخدمة لكي نبقيك على اطلاع حول محتوى الملف الذي ستقوم بتحميله .
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