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`

Answer

6

Explanation

Here `vecOA = veca, vecOB= 10veca + 2vecb ,vecOC =vecb`
q= Area of parallelogram with OA and OC as adjacent sides.
`q= |veca xx vecb|`
P= Area of quadrilateral OABC
= Area of `triangleOAB + " Area of " triangleOBC`
`1/2|vecaxx(10 veca + 2vecb)|+1/2|(10veca + 2vecb)xx vecb|`
`= |veca xx vecb|+5|veca xx vecb|`
`p =6 |vecaxxvecb|`
or p= 6 q
k=6