#### Question

By vector method show that the quadrilateral with vertices A (1, 2, –1), B (8, –3, –4), C (5, –4, 1), D (–2, 1, 4) is a parallelogram.

#### Solution

Let `bara,barb,barc and bard` be the position vectors of vertices A, B, C, D respectively

∴From (i) and (ii), we get

`bare= barf`

The mid point of the diagonals AC and BD is same

∴ The diagonals AC and BD bisect each other.

∴ The `square`ABCD is a Parallelogram.

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#### APPEARS IN

Solution for question: By vector method show that the quadrilateral with vertices A (1, 2, –1), B (8, –3, –4), C (5, –4, 1), D (–2, 1, 4) is a parallelogram. concept: Vectors - Diagonals of a Parallelogram Bisect Each Other and Converse. For the courses HSC Arts, HSC Science (Electronics), HSC Science (General) , HSC Science (Computer Science)