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Let vec O A= vec a , hat O B=10 vec a+2...

Let ` vec O A= vec a , hat O B=10 vec a+2 vec ba n d vec O C= vec b ,w h e r eO ,Aa n dC` are non-collinear points. Let `p` denotes the areaof quadrilateral `O A C B ,` and let `q` denote the area of parallelogram with `O Aa n dO C` as adjacent sides. If `p=k q ,` then find`kdot`

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The correct Answer is:
6
q= Area of parallelogram with `vec(OA) and vec(OC)` as adjacent sides
`|vec(OA) xx vec(OC)|`
`|veca xx vecb|`
p = Area of quadrilateral OABC
`1/2|vec(OA)xx vec(OB)|+1/2|vec(OB)xx vec(OC)|`
`1/2[|veca xx(10 veca + 2vecb)|+|(10veca + 2vecb)xxvecb|]`
`1/2|(12veca xx vecb)|=6|veca xx vecb| Rightarrow k =6`
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