The position vectors of the points A, B, C of a parallelogram ABCD are a, b, and c respectively. How do I express, in terms of a, b and, the position vector of D?

1 Answer
Aug 5, 2018

a+c-ba+cb.

Explanation:

Suppose that, the position vector (pv) of the point DD is dd.

We dnote this by D=D(d)D=D(d).

Now, we know from Geometry that, the diagonals ACAC and BDBD

of a parallelogram ABCDABCD bisect each other.

Therefore, the mid-point of the diagonal ACAC is the same as that of

the diagonal BDBD.

But, the pv. of ACAC is (a+c)/2a+c2, &, that of BD, (b+d)/2BD,b+d2.

:. (a+c)/2=(b+d)/2.

Clearly, d=a+c-b.

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