Home
Class 12
MATHS
Let vec a, vec b, and vec c be three non...

Let `vec a, vec b, and vec c` be three non coplanar unit vectors such that the angle between every pair of them is `pi/3`. If `vec a xx vec b+ vecb xx vec x=p vec a + q vec b + r vec c` where p,q,r are scalars then the value of `(p^2+2q^2+r^2)/(q^2)` is

Text Solution

Verified by Experts

The correct Answer is:
`(4)`
`|veca|=|vecb|=|vecc|=1`
` veca.vecb=vecb. vecc=vecc.veca=1//2`
Also ` vecaxxvecb+vecbxxvecc=pveca+qvecb+rvecc`
`implies veca.(vecbxxvecc) = p +q(veca.vecb) +r(veca.vecc)`
`implies veca.(vecbxxvecc ) = p+q(veca.vecb) r(veca.vecc)`
`therefore p+(q)/(2)+(r)/(2)=[vecavecbvecc]`
similarly taking dot product with vector `vecb` , we get
`(p)/(2)+q+(r)/(2)=0`
And, taking dot product with vector `vecc`, we get
`(p)/(2)+(q)/(2)+r=[veca vecbvecc]`
solving,(1),(2) and (3) , we get
` p=r=-q`
`implies (p^(2)+2q^(2)+r^(2))/(q^(2))=4`
Promotional Banner

Similar Questions

Explore conceptually related problems

Let vec a , vec b ,a n d vec c be non-coplanar unit vectors, equally inclined to one another at an angle theta . If vec axx vec b+ vec bxx vec c=p vec a+q vec b+r vec c , find scalars p ,qa n dr in terms of thetadot

If vec a , vec b ,a n d vec c are three non-coplanar non-zero vecrtors, then prove that ( vec a . vec a) vec bxx vec c+( vec a . vec b) vec cxx vec a+( vec a . vec c) vec axx vec b=[ vec b vec c vec a] vec a

Show that (vec a - vec b) xx (vec a + vec b) = 2 (vec a xx vec b)

Let vec a , vec b , vec c be three unit vectors and vec a . vec b= vec a . vec c=0. If the angel between vec b and vec c is pi/3 , then find the value of |[ vec a vec b vec c]| .

If vec a , vec b and vec c are non-coplanar vectors, prove that vectors 3vec a-7 vec b-4 vec c ,3 vec a -2 vec b+ vec c and vec a + vec b +2 vec c are coplanar.

If vec a, vec b, vec c are unit vectors such that vec a+ vec b+ vec c =0 , find the value of vec a.vec b+ vec b .vec c + vec c. vec a .

If vec a , vec ba n d vec c are three non-coplanar vectors, then ( vec a+ vec b+ vec c)dot[( vec a+ vec b)xx( vec a+ vec c)] equals a. 0 b. [ vec a vec b vec c] c. 2[ vec a vec b vec c] d. -[ vec a vec b vec c]

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

If vec a ,a n d vec b be two non-collinear unit vector such that vec axx( vec axx vec b)=1/2 vec b , then find the angle between vec a ,a n d vec bdot

If vec a , vec ba n d vec c are unit coplanar vectors, then the scalar triple product [2 vec a- vec b2 vec b- vec c2 vec c- vec a] is a. 0 b. 1 c. -sqrt(3) d. sqrt(3)