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?

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Answer 1 · 2018-08-05T04:52:13

$a+c-b$ .

Suppose that, the position vector (pv) of the point $D$ is $d$ .

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

Now, we know from Geometry that, the diagonals $AC$ and $BD$

of a parallelogram $ABCD$ bisect each other.

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

the diagonal $BD$ .

But, the pv. of $AC$ is $(a+c)/2$ , &, that of $BD, (b+d)/2$ .

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

Clearly, $d=a+c-b$ .

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