The adjacent sides of a paralellelogram is given by two vector A and B where `A=5hati-4hatj+3hatkand B=3hati-2hatj+hatk` Calulate the aera of parallelogram .

Options

A. `10sqrt(30) "sq units"`
B. `100sqrt(3) "sq units"`
C. `10sqrt(3) "sq units"`
D. `10sqrt(2) "sq units"`

Answer

C

Explanation

Here ,A and B repesents the adjacent side o d a parallelogram.

`A=5hati -4hatj+3hatk`
`B=3hati-2hatj+hatk`
Aera of parallelogrm `=|AxxB|`
`AxxB=|underset(3,-2,-1)underset(5,-4,3)hati,hatj,hatk|`
`=hati(4+6)-hatj(-5-9)+hatk(-10+12)`
`=10hati+14hatj+2hatk`
`implies |AxxB|=sqrt((10)^(2)+(14)^(2)+(2)^(2))`
` =sqrt(300) =10sqrt(3) "sq units"`