Home
Class 12
MATHS
If the vectors vec a and vec bare linear...

If the vectors `vec a` and `vec b`are linearly independent and satisfying `(sqrt3tantheta-1)vec a + (sqrt3sectheta-2)vec b=vec 0`,then the most general values of `theta` are:

A

`npi+(pi)/(6),n inZ`

B

`2npi+-(11pi)/(6)n in Z`

C

`n pi+-(pi)/(6),n in Z`

D

`2npi+(11pi)/(6), n in Z`

Text Solution

Verified by Experts

The correct Answer is:
D
`sqrt(3) tan theta+1 =0 and sqrt(3) sec theta-2=0`
`implies theta=(11pi)/(6)`
`implies theta=2n pi+(11pi)/(6), n in Z`.
Promotional Banner

Similar Questions

Explore conceptually related problems

If |vec(A)xxvec(B)|=sqrt(3)vec(A).vec(B) , then the value of |vec(A)+vec(B)| is

If vec a , vec b are any two vectors, then give the geometrical interpretation of g relation | vec a+ vec b|=| vec a- vec b|

The direction of vector vec(b) is North-East and that vec( c ) is North-West |vec(b)|=|vec( c )|=4 . If vec(a)=vec( c )-vec(b) then the magnitude and direction of the vectors vec(a) are …………….

The non-zero vectors are vec a,vec b and vec c are related by vec a= 8vec b and vec c = -7vec b . Then the angle between vec a and vec c is

The non-zero vectors are vec a,vec b and vec c are related by vec a= 8vec b and vec c = -7vec b . Then the angle between vec a and vec c is

If vec x and vec y are two non-collinear vectors and a triangle ABC with side lengths a,b,c satisfying (20a-15b)vec x+(15b-12c)vec y+(12c-20a)(vec x xx vec y) = vec0 . Then triangle ABC is:

Let vec(a),vec(b) and vec( c ) are three unit vectors such that vec(a)xx(vec(b)xx vec( c ))=(sqrt(3))/(2)(vec(b)+vec( c )) . If the vectors vec(b) and vec( c ) are not parallel then the angle between vec(a) and vec(b) is ……….

The unit vectors vec(a),vec(b) and vec( c ) are not coplanar. If vec(a)xx(vec(b)xx vec( c ))=(1)/(sqrt(2))(b+c) then the angle between vec(a) and vec(b) is ………………

If vec(a).vec(a)=0 and vec(a).vec(b)=0 then what can be concluded about the vector vec(b) ?