Let `vec(OA) =veca, vecOB = 10 veca + 2vecb and vecOC =vecb` , where O,A and C are non- collinear points. Let P denote the area of quadrilateral OACB. And let q denote the area of parallelogram with OA nad OC as adjacent sides. If `p = k q` , then find k .

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