Home
Class 12
MATHS
If alpha(veca xx vecb)+beta(vecb xx vecc...

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

A

`veca,vecb,vecc` are coplanar is all `alpha,beta, gamma ne0`

B

`veca,vecb,vec` are coplanar if any one of `alpha, beta, gamma ne0`

C

`veca,vecb,vecc` are non-coplanar for any `alpha,beta,gamma ne0`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A, B
we have,
`alpha(veca xx vecb) +beta(vecb xx vecc) + lambda(vecc xx veca)=0`
Taking dot product with `vecc`, we have
`alpha[vecavecbvecc]=0`
Similarly, taking dot product with b and c, we have `lamba[vecavecbvecc]=0, beta[vecavecbvecc]=0`
Now, even if one of `alpha, beta, lambda ne 0`, then we have `[vecavecbvecc]=0`
`rArr veca,vecb,vecc` are coplanar
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE|Exercise JEE Previous Year|12 Videos

  • SEQUENCE AND SERIES

    CENGAGE|Exercise Question Bank|1 Videos

Similar Questions

Explore conceptually related problems

Let veca, vecb, and vecc be three non- coplanar vectors and vecd be a non -zero , which is perpendicular to (veca + vecb + vecc). Now vecd = (veca xx vecb) sin x + (vecb xx vecc) cos y + 2 (vecc xx veca) . Then

If veca , vecb and vecc are three vectors such that vecaxx vecb =vecc, vecb xx vecc= veca, vecc xx veca =vecb then prove that |veca|= |vecb|=|vecc|

Let vecr = (veca xx vecb)sinx + (vecb xx vecc)cosy+(vecc xx veca) , where veca,vecb and vecc are non-zero non-coplanar vectors, If vecr is orthogonal to 3veca + 5vecb+2vecc , then the value of sec^(2)y+"cosec"^(2)x+secy" cosec "x is

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

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

Unit vectors veca and vecb ar perpendicular , and unit vector vecc is inclined at an angle theta to both veca and vecb . If alpha veca + beta vecb + gamma (veca xx vecb) then.

if veca=hati+hatj+2hatk, vecb=hati+2hatj+2hatk and |vecc|=1 Such that [veca xx vecb vecb xx vecc vecc xx veca] has maximum value, then the value of |(veca xx vecb) xx vecc|^(2) is

Let veca and vecc be unit vectors inclined at pi//3 with each other. If (veca xx (vecb xx vecc)). (veca xx vecc)=5 , then [vecavecbvecc] is equal to

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 .