Let P(1,2,1), Q(1,0,-1), R(2,2,0) be the vertices of a parallelogram with adjacent sides PQ and PR. Find the other vertex S.

Given:

The vertices of a parallelogram are P(1,2,1), Q(1,0,-1), R(2,2,0).

PQ and PR are the adjacent sides of the parallelogram.

To find:

The coordinates of vertex S.

Solution:

We know that, the diagonals of a parallelogram bisect each other.

Let the coordinates of the vertex S are (a,b,c).

In the given parallelogram PS and QR are the diagonals. It means their midpoints are same.

On comparing both sides, we get

Similarly,

And,

Therefore, the coordinates of vertex S are (2,0,-2).

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step-by-step explanation: