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3D Coordinate Geometry

3D Section Formula


What are the coordinates of PP which divide the line segment joining the points A=(4,4,1)A=(-4,4,1) and B=(4,4,2)B=(4,-4,2) in the ratio 3:2?3:2 ?

Let A(4,3,5) A ( 4, 3, 5 ) and B(2,6,0) B ( 2, 6 , 0) be two fixed points. Find the position vector of the point which lies on the line segment AB \overline{AB} and internally divides it in the ratio 7:8. 7 : 8.

The above rectangular cuboid has base dimensions a=12a=12 and b=8.b=8. If the centroid II of triangle ACFACF internally divides the diagonal BH\overline{BH} of the rectangular cuboid in the ratio BI:IH=1:m,BI:IH=1:m, what is the value of m?m?

Suppose three vertices of a parallelogram are O=(0,0,0),A=(1,5,6),B=(1,5,5),O=(0,0,0), A=(1,5,6), B=(-1,-5,5), where OA\overline{OA} and OB\overline{OB} are adjacent sides. If CC is the final vertex of the parallelogram, then what are the coordinates of C?C ?

Consider a triangle ABCABC such that the centroid of of the triangle is G=(5,2,3)G=(5,-2,3) and the midpoint of AB\overline{AB} is P=(1,12,12).P=\left(1,\frac{1}{2},\frac{1}{2}\right). What are the coordinates of the point C?C ?


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