i. If vec a , vec b and vec c are ...

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

Topper's Solved these Questions

TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS
CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|6 Videos
VECTORS TRIPLE PRODUCTS, RECIPROCAL SYSTEM OF VECTORS
CENGAGE PUBLICATION|Exercise DPP 2.4|20 Videos

Similar Questions

Explore conceptually related problems

If vec a , vec ba n d vec c are three non coplanar vectors, then ( veca + vecb + vecc )[( veca + vecb )×( veca + vecc )] is :

If vec a , vec b and vec c are any three non-coplanar vectors, then prove that points are collinear: veca+ vecb+vecc , 4veca+3vecb ,10veca+7vec b-2vecc .

If veca, vecb and vecc are three non-coplanar non-zero vectors, then prove that (veca.veca) vecb xx vecc + (veca.vecb) vecc xx veca + (veca.vecc)veca xx vecb = [vecb vecc veca] veca

For any four vectors, prove that ( veca × vecb )×( vecc × vecd )=[ veca vecc vecd ] vecb −[ vecb vecc vecd ] veca

If veca xx vecb + vecb xx vecc + vecc xx veca = 0 . Show that the vectors veca, vecb, vecc are coplanar.

If veca , vecb and vecc are non- coplanar vectors and veca xx vecc is perpendicular to veca xx (vecb xx vecc) , then the value of [ veca xx ( vecb xx vecc)] xx vecc is equal to

If a ,ba n dc are three non-cop0lanar vector, non-zero vectors then the value of ( veca . veca ) vecb × vecc +( veca . vecb ) vecc × veca +( veca . vecc ) veca × vecb .

vec a , vec ba n d vec c are three non-coplanar ,non-zero vectors and vec r is any vector in space, then ( veca × vecb )×( vecr × vecc )+( vecb × vecc )×( vecr × veca )+( vecc × veca )×( vecr × vecb ) is equal to

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

If veca , vecb , vecc are three mutually perpendicular unit vectors, then prove that ∣ veca + vecb + vecc | = sqrt3

CENGAGE PUBLICATION-VECTOR ALGEBRA-All Questions

The median AD of the triangle ABC is bisected at E and BE meets AC at ...
Text Solution
|
Vectors vec a and vec b are non-collinear. Find for what value of...
Text Solution
|
i. If vec a , vec b and vec c are non-coplanar vectors, prove th...
Text Solution
|
Prove that a necessary and sufficient condition for three vectors ...
Text Solution
|
If vec a , vec b , vec ca n d vec d are distinct vectors such that ...
Text Solution
|
If vec a , vec ba n d vec c are non-coplanar vectors, prove that the ...
Text Solution
|
Find the unit vector in the direction of the vector vec a= hat i+ ...
Text Solution
|
let P an interioer point of a triangle A B C and A P ,B P ,C P meets t...
Text Solution
|
Let vec a , vec ba n d vec c be unit vectors, such that vec a+ vec b...
Text Solution
|
Let vec A and vec B be two non-parallel unit vectors in a plane. If...
Text Solution
|
If the vectors 3 vec p+ vec q ;5p-3 vec qa n d2 vec p+ vec q ;4 vec p-...
Text Solution
|
P(1,0,-1), Q(2,0,-3),R(-1,2,0)a n dS(3,-2,-1), then find the projectio...
Text Solution
|
A , B , C , D are any four points, prove that vec A Bdot vec C D+ v...
Text Solution
|
Let vec u=hat(i)+hat(j), vec v=hat(i)-hat(j) and vec w=hat(i)+2hat(j)+...
Text Solution
|
If the angel between unit vectors vec aa n d vec b60^0 , then find...
Text Solution
|
veca+vecb+vecc=vec0, |veca|=3, |vecb|=5,|vecc|=9,find the angle betwee...
Text Solution
|
Constant forces P1= hat i+ hat j+ hat k ,P2= - hat i+2 hat j- hat ka n...
Text Solution
|
If vec a , a n d vec b are unit vectors , then find the greatest v...
Text Solution
|
Let G1, G2a n dG3 be the centroids of the triangular faces O B C ,O ...
Text Solution
|
Prove that hat(i)times(vec atimeshat(i))+hat(j)times(vec atimeshat(j))...
Text Solution
|