The diagonals of a parallelogram are `2hati` and `2hatj`. What is the area of the parallelogram

Options

A. 0.5 unit
B. 1 unit
C. 1.5 unit
D. 2 units

Answer

D

Explanation

Let `vec P and vec Q` be the sides of the parallelogram.
Them `vec P + vec Q =2hati and vec P - vec Q =2 hatj`
`therefore 2vec P =2hati +2hatj" or "vec P = hati+hatj`
`therefore hati +hatj + vec Q = 2hati" "therefore vec Q =hati-hatj`

Area of a parallelogram
`=|PxxQ|=|(hati+hatj)xx (hati-hatj)|`
`=|(-ixxj)+(vec j xx vec i)|=|-hatk=hatk|=|-2hatk|`
`therefore` Area = 2 units