Let `vec(OA) =veca, vec(OB) = 10veca + 2vecb and vec(OC) =vecb` where , O, A and C are non-collinear points. Let p denote that area of the quadrilateral OABC. And let q denote the area of the parallelogram with OA and OC as adjacent sides. If p=kq, then k= _________

Answer

6

Explanation

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`