If O is the origin and P(x(1),y(1)), Q(x...

If O is the origin and `P(x_(1),y_(1)), Q(x_(2),y_(2))` are two points then `OPxOQ sin angle POQ=`

`x_(1)y_(2)+x_(1)y_(2)`

`x_(1)y_(2)+x_(2)y_(1)`

`|x_(1)y_(2)-x_(2)y_(1)|`

none of these

Text Solution

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The correct Answer is:

We have,
Area of `DeltaOPQ`= Absoulte value of `(1)/(2)|{:(0,0,0),(x_(1),y_(1),1),(x_(2),y_(2),1):}|`
`rArr"Area of" DeltaOPQ=(1)/(2)|x_(1)y_(2)-x_(2)y_(1)|`
Also, Area of `DeltaOPQ=(1)/(2)OPxxOQxx sin anglePOQ`
`:.(1)/(2) OPxxOQ sin anglePOQ=(1)/(2)|x_(1)y_(2)-x_(2)y_(1|`
`rArr OPxxOQ sin angle POQ =|x_(1)y_(2)-x_(2)y_(2)|`

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