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#.

#color(violet)("Enjoy Maths.!")#