Home
Class 12
MATHS
Let vec(alpha)=ahati+bhatj+chatk, vec(be...

Let `vec(alpha)=ahati+bhatj+chatk, vec(beta)=bhati+chatj+ahatk` and `vec(gamma)=chati+ahatj+bhatk` be three coplnar vectors with `a!=b`, and `vecv=hati+hatj+hatk`. Then `vecv` is perpendicular to

A

`vecalpha+vecbeta`

B

`vecbeta+vecgamma`

C

`vecgamma+vecalpha`

D

`vecalpha+vecbeta+vecgamma`

Text Solution

Verified by Experts

The correct Answer is:
1,2,3,4
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • VECTOR ALGEBRA

    AAKASH INSTITUTE|Exercise ASSIGNMENT (SECTION-D) Comprehesion-I|3 Videos

  • VECTOR ALGEBRA

    AAKASH INSTITUTE|Exercise ASSIGNMENT (SECTION-D) Comprehesion-II|3 Videos

  • VECTOR ALGEBRA

    AAKASH INSTITUTE|Exercise ASSIGNMENT (SECTION-B)|32 Videos

  • TRIGNOMETRIC FUNCTIONS

    AAKASH INSTITUTE|Exercise Section - J (Akash Challengers Question)|15 Videos

Similar Questions

Explore conceptually related problems

If vec(a) = hati - 2hatj - 3hatk, vec(b) = 2hati +hatj - hatk and vec(c) = hati +3hatj - 2hatk then find vec(a) xx (vec(b) xx vec(c)) .

If vec(a) = hati - 2hatj - 3hatk, vec(b) = 2 hati - hatj - hatk and vec(c) = hati +3 hatj - 2hatk find (vec(a) xx vec(b)) xx vec(c)

Knowledge Check

  • Let vec(alpha)=ahati+bhatj+chatk,vecb=bhati+chatj+ahatk and vec(gamma)=chati+ahatj+bhatk are three coplanar vectors with a!=b and vec(gamma)=hati+hatj+hatk . Then vec(gamma) is perpendicular to

    A
    `vec(alpha)`
    B
    `vec(beta)`
    C
    `vec(gamma)`
    D
    all of these

  • If veca =hati + hatj - hatk, vecb = 2hati + 3hatj + hatk and vec c = hati + alpha hatj are coplanar vector , then the value of alpha is :

    A
    `-4/3`
    B
    `3/4`
    C
    `4/3`
    D
    `2`

  • Let vec(a)=2hati-hatj+hatk,vec(b)=hati+2hatj-hatk and vec( c )=hati+hatj-2hatk be three vectors. A vector in the plane of vec(b) and vec( c ) whose projection on vec(a) is of magnitude sqrt(2//3) is

    A
    `2hati+3hatj-3vec(b)`
    B
    `2hati+3hatj+3hatk`
    C
    `-2hati-hatj+5hatk`
    D
    `2hati+hatj+5hatk`

    • Similar Questions

    Explore conceptually related problems

    If vec(OA)=2hati-hatj+hatk, vec(OB)=hati-3hatj-5hatk and vec(OC)=3hati-3hatj-3hatk then show that CB is perpendicular to AC.

    Prove that the vectors vec(A) = 2hati - 3hatj - hatk and vec(B) =- 6 hati + 9hatj +3hatk are parallel.

    What is the projection of vec(A) = hati + hatj+ hatk on vec(B) = (hati + hatk)

    If vec(alpha)=2hati+3hatj-hatk, vec(beta)=-hati+2hatj-4hatk, vecgamma=hati+hatj+hatk , then (vec(alpha)xxvec(beta)).(vec(alpha)xxvec(gamma)) is equal to

    Let a be a real number and vec alpha = hati +2hatj, vec beta=2hati+a hatj+10 hatk, vec gamma=12hati+20hati+a hatk be three vectors, then vec alpha, vec beta and vec gamma are linearly independent for :

    Home
    Profile