Home
Class 12
MATHS
Let veca, vecb and vecc are three unit v...

Let `veca, vecb` and `vecc` are three unit vectors in a plane such that they are equally inclined to each other, then the value of `(veca xx vecb).(vecb xx vecc) + (vecb xx vecc). (vecc xx veca)+(vecc xx veca). (veca xx vecb)` can be

A

`9/4`

B

`-9/4`

C

`3/4`

D

`-3/4`

Text Solution

Verified by Experts

The correct Answer is:
A
Since `veca, vecb` and `vecc` are in a plane and equally inclined to each other, then angle between any two vectors is `120^(@)` and `(veca xx vecb), (vecb xx vecc)` and `(vecc xx veca)` are parallel.
So, `(veca xx vecb).(vecb xx vecc) = |veca xx vecb||vecb xx vecc|.costheta`
`=sqrt(3)/2.sqrt(3)/2.1=3/4`
Similarly, `(vecb xx vecc). (vecc xx veca) = 3/4` and `(vecc xx veca).(veca xx vecb) =3/4`
`rArr "sum"=3/4+3/4+3/4=9/4`
Promotional Banner

Topper's Solved these Questions

  • COORDINATE SYSYEM

    CENGAGE|Exercise JEE Main Previous Year|6 Videos

  • CURVE TRACING

    CENGAGE|Exercise Exercise|24 Videos

Similar Questions

Explore conceptually related problems

Show that (veca xx vecb) *(vecc xx vecd) +(vecb xx vecc) *(veca xx vecd) +(vecc xx veca) *(vecb xx vecd)=0 .

If alpha(veca xx vecb)+beta(vecb xx vecc)+gamma(vecc xx veca)=0 , then

If veca, vecb and vecc are three units vectors equally inclined to each other at an angle alpha . Then the angle between veca and plane of vecb and vecc is

If veca + 2 vecb + 3 vecc = vec0 " then " veca xx vecb + vecb xx vecc + vecc xx veca=

for any three vectors, veca, vecb and vecc , (veca-vecb) . (vecb -vecc) xx (vecc -veca) = 2 veca.vecb xx vecc .

Vectors veca, vecb, vecc are three unit vectors and vecc is equally inclined to both veca and vecb . Let veca xx (vecb xx vecc) + vecb xx (vecc xx veca) =(4+x^(2))vecb-(4xcos^(2)theta)veca , then veca and vecb are non-collinear vectors, x gt 0

if veca xx vecb = vecc,vecb xx vecc = veca , " where " vecc ne vec0 then

If vectors, vecb, vcec and vecd are not coplanar, the pove that vector (veca xx vecb) xx (vecc xx vecd) + ( veca xx vecc) xx (vecd xx vecb) + (veca xx vecd) xx (vecb xx vecc) is parallel to veca .

If [ veca vecbvecc]=2 , then find the value of [(veca+2vecb-vecc) (veca - vecb) (veca - vecb-vecc)]