Home
Class 11
MATHS
Let vec u a n d vec v be unit vectors s...

Let ` vec u a n d vec v` be unit vectors such that ` vec uxx vec v+ vec u= vec w` and ` vec wxx vec u= vec vdot` Find the value of `[ vec u vec v vec w]dot`

Text Solution

Verified by Experts

The correct Answer is:
1
Given , `vecu xx vecv + vecu = vecw and vecw xx vecu = vecv`
`Rightarrow (vecu xx vecv + vecu) xx vecu = vecv`
` Rightarrow ( vecu xx vecv) xx vecu = vecv`
`Rightarrow vecv - (vecu.vecv)= vecv`
`Rightarrow (vecu.vecv)vecu = 0 Rightarrow (vecu vecv) =0`
Now `[vecu vecv vecq] = vecu. (vecv xx vecw)`
` vecu . (vecu xx (vecu xx vecv) +vecv xx vecu)`
`vecu (vecv^(2) vecu- (vecu.vecv) vecv + vecv xx vecu) = vecv^(2) vecu^(2) =1`
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

Let vec u , vec va n d vec w be vectors such that vec u+ vec v+ vec w=0. If | vec u|=3,| vec v|=4a n d| vec w|=5, then vec udot vec v+ vec vdot vec w+ vec wdot vec u is a. 47 b. -25 c. 0 d. 25

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 ,a n d vec c are three vectors such that vec axx vec b= vec c , vec bxx vec c= vec a , vec cxx vec a= vec b , then prove that | vec a|=| vec b|=| vec c|dot

Let vec aa n d vec b be unit vectors such that | vec a+ vec b|=sqrt(3) . Then find the value of (2 vec a+5 vec b)dot(3 vec a+ vec b+ vec axx vec b)dot

If vec aa n d vec b are two vectors, then prove that ( vec axx vec b)^2=| vec adot vec a vec adot vec b vec bdot vec a vec bdot vec b| .

Let vec a , vec b ,a n d vec c be any three vectors, then prove that [ vec axx vec b vec bxx vec c vec cxx vec a]=[ vec a vec b vec c]^2dot

Given | vec a|=| vec b|=1a n d| vec a+ vec b|=sqrt(3). If vec c is a vector such that vec c- vec a-2 vec b=3( vec axx vec b), then find the value of vec c dot vec b

Let vec a , vec ba n d vec c be unit vectors, such that vec a+ vec b+ vec c= vec x , vec adot vec x=1, vec bdot vec x=3/2,| vec x|=2. Then find the angel between cc and xxdot

If | vec a|=| vec b|=| vec a+ vec b|=1, then find the value of | vec a- vec b|dot

If vec a and vec b are two vectors such that | vec axx vec b|=2, then find the value of [ vec a vec b vec axx vec b].