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.

Explanation

The points `A(4,5,10), B(2,3,4)` and `C(1,2,-1)` are three vertices of parallelogram ABCD.


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


Direction vector along `A B` is


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`vec{a}=(2-4) hat{i}+(3-5) hat{j}+(4-10) hat{k}=-2 hat{i}-2 hat{j}-6 hat{k}`


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`therefore` Equation of line `A B`, is given by


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