Q25 of 46 Page 1

The points A(4, 5, 10), B(2, 3, 4) and C (1, 2, - 1) are three vertices of a parallelogram ABCD. Find the vector equations of the sides AB and BC and also find the coordinates of point D.

Let the coordinates of D be (x,y,z)


Direction vector along AB is




∴ Equation of line AB is:



Direction vector along BC is




∴ Equation of line BC is:



Since ABCD is a parallelogram AC and BD bisect each other.



⇒ 2 + x = 5, 3 + y = 7, 4 + z = 9


⇒ x = 3, y = 4, z = 5


Coordinates of D are (3,4,5).


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