Home
Class 11
MATHS
Points vec a , vec b , vec c ,a n d vec...

Points ` vec a , vec b , vec c ,a n d vec d` are coplanar and `(s inalpha) vec a+(2sin2beta) vec b+(3sin3gamma) vec c- vec d=0.` Then the least value of `sin^2alpha+sin^2 2beta+sin^2 3gammai s` `1/(14)` b. `14` c. `6` d. `1//sqrt(6)`

A

`1//14`

B

14

C

6

D

`1//sqrt6`

Text Solution

Verified by Experts

The correct Answer is:
a
Points `veca , vecb , vecc and vecd` are coplanar, therefore,
`sin alpha + 2 sin 2 beta + 3 sin 3 gamma =1 `
` now |sin alpha + 2sin 2 beta + 2sin 3 gamma|`
`le sqrt(1+4+9). sqrt(sin^(2)alpha +sin^(2)2beta + sin^(2) 3gamma)`
`or sin ^(2) alpha + sin^(2) 2beta + sin ^(2) 3 gamma le 1/14`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise 2.1|18 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise 2.2|15 Videos

  • CONIC SECTIONS

    CENGAGE|Exercise Solved Examples And Exercises|1255 Videos

  • LIMITS AND DERIVATIVES

    CENGAGE|Exercise Solved Examples And Exercises|288 Videos

Similar Questions

Explore conceptually related problems

Points vec a , vec b , vec c ,a n d vec d are coplanar and (sinalpha) vec a+(2sin2beta) vec b+(3sin3gamma) vec c- vec d=0. Then the least value of sin^2alpha+sin^2 2beta+sin^2 3gammai s a. 1/(14) b. 14 c. 6 d. 1//sqrt(6)

Prove that [ vec a, vec b, vec c + vec d] = [ vec a, vec b, vec c] + [ vec a, vec b , vec d] .

If [ vec a vec b vec c]=2, then find the value of [( vec a+2 vec b- vec c)( vec a- vec b)( vec a- vec b- vec c)]dot

If vec a , vec b ,a n d vec c are mutually perpendicular vectors and vec a=alpha( vec axx vec b)+beta( vec bxx vec c)+gamma( vec cxx vec a)a n d[ vec a vec b vec c]=1, then find the value of alpha+beta+gammadot

Vectors vec a and vec b are non-collinear. Find for what value of n vectors vec c=(n-2) vec a+ vec b and vec d=(2n+1) vec a- vec b are collinear?

If vectors vec a , vec b ,a n d vec c are coplanar, show that | vec a vec b vec c vec adot vec a vec adot vec b vec adot vec c vec bdot vec a vec bdot vec b vec bdot vec c|=0

If vec a , vec ba n d vec c are unit vectors satisfying | vec a- vec b|^2+| vec b- vec c|^2+| vec c- vec a|^2=9, then |2 vec a+5 vec b+5 vec c| is.

Let vec a , vec ba n d vec c be pairwise mutually perpendicular vectors, such that | vec a|=1,| vec b|=2,| vec c|=2. Then find the length of vec a+ vec b+ vec c

If vec a , vec b , vec ca n d vec d are distinct vectors such that vec axx vec c= vec bxx vec da n d vec axx vec b= vec cxx vec d , prove that ( vec a- vec d)dot (vec b- vec c)!=0,

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