Home
Class 11
MATHS
Let vec O A- vec a , vec O B=10 vec a+2...

Let ` vec O A- vec a , vec 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`

Text Solution

Verified by Experts

The correct Answer is:
6
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
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise 2.1|18 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise 2.2|15 Videos

  • CONIC SECTIONS

    CENGAGE|Exercise Solved Examples And Exercises|1255 Videos

  • LIMITS AND DERIVATIVES

    CENGAGE|Exercise Solved Examples And Exercises|288 Videos

Similar Questions

Explore conceptually related problems

Let overset(to)(OA) = overset(to)(a), vec(OB)= 10vec(a) + 2vec(b) " and " overset(to)(OC)=overset(to)(b) where O,A and C are non-collinear points . Let P denotes the area of the quadrilateral OABC and let q denots the area of the parallelogram with OA and OC as adjacent sides. If p =kq , then k=........

If | vec a|+| vec b|=| vec c|a n d vec a+ vec b= vec c , then find the angle between vec aa n d vec bdot

If vec A O+ vec O B= vec B O+ vec O C , then A ,Bn a dC are (where O is the origin) a. coplanar b. collinear c. non-collinear d. none of these

if vec Ao + vec O B = vec B O + vec O C ,than prove that B is the midpoint of AC.

Statement 1: In "Delta"A B C , vec A B+ vec BC+ vec C A=0 Statement 2: If vec O A= vec a , vec O B= vec b ,t h e n vec A B= vec a+ vec b

If three unit vectors vec a , vec b ,a n d vec c satisfy vec a+ vec b+ vec c=0, then find the angle between vec aa n d vec bdot

If vec axx vec b= vec bxx vec c!=0,w h e r e vec a , vec b ,a n d vec c are coplanar vectors, then for some scalar k prove that vec a+ vec c=k vec bdot

If 2 vec A C = 3 vec C B , then prove that 2 vec O A =3 vec C B then prove that 2 vec O A + 3 vec O B =5 vec O C where O is the origin.

Let vec a , vec ba n d vec c be unit vectors, such that vec a+ vec b+ vec c= vec x , vec adot vec x=1, vec bdot vec x=3/2,| vec x|=2. Then find the angel between cc and xxdot

Let vec a , vec b ,a n d vec c be any three vectors, then prove that [ vec axx vec b vec bxx vec c vec cxx vec a]=[ vec a vec b vec c]^2dot