Home
Class 12
MATHS
If vec x and vecy are unit vectors and |...

If `vec x and vecy` are unit vectors and `|vecz| = 2/sqrt7` such that `vecz + (vecz xx vecx) = vecy` then find the angle `theta` between `vecx and vecz`

Text Solution

Verified by Experts

`vecz+vecz xx vecx = vecy or |vecz + veczxxvecx|^(2)= |vecy|^(2)`
or `|vecz|^(2)+ |vecz|^(2)|vecx|^(2)sin^(2) theta =1`
(because `vecz. (veczxx vecx) =0`)
`or |vecz|^(2) (1 + sin theta ) =1`
`or |vecz|^(2) = 1/(sqrt(1+sin^(2) theta))= 2/sqrt7`
`or sin theta = sqrt3//2`
`Rightarrow theta = pi//3 = 60^(@)`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Exercise 2.3|18 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Exercises|15 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Exercise 2.1|18 Videos

  • DETERMINANTS

    CENGAGE PUBLICATION|Exercise All Questions|262 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|578 Videos

Similar Questions

Explore conceptually related problems

If vec a and vec b be two non-collinear unit vector such that vec axx( vec axx vec b)=1/2 vec b , then find the angle between vec a and vec b .

Two vectors vec(a) and vec (b) are such that |vec(a).vec(b)| = |vec(a) xx vec(b)| , then find the angle between the vectors vec(a) and vec(b) .

If three unit vectors vec a , vec b , and vec c satisfy vec a+ vec b+ vec c=0, then find the angle between vec a and vec bdot

If vec a and vec b are unequal unit vectors such that ( vec a- vec b)xx[( vec b+ vec a)xx(2 vec a+ vec b)]= vec a+ vec b , then angle theta between vec aa n d vec b is 0 b. pi//2 c. pi//4 d. pi

If vec a , vec b and vec c are non-coplanar unit vectors such that vec axx( vec bxx vec c)=( vec b+ vec c)/(sqrt(2)) , then the angle between vec a and vec b is a. 3pi//4 b. pi//4 c. pi//2 d. pi

If veca and vecb are unequal unit vectors such that (veca - vecb) xx[ (vecb + veca) xx (2 veca + vecb)] = veca+vecb then angle theta " between " veca and vecb is

If vec a and vec b are unit vectors such that ( vec a+ vec b).[(2 vec a+3 vec b)xx(3 vec a-2 vec b)]=0 , then angle between veca and vec b is

If vec a\ a n d\ vec b are two vectors such that | vec axx vec b|=sqrt3\ a n d\ vec adot vec b=1, find the angle between vec a\ a n d\ 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 a dot vec x=1, vec b dot vec x=3/2,| vec x|=2. Then find the angle between vec c and vec x

If three unit vectors veca, vecb and vecc " satisfy" veca+vecb+vecc= vec0 . Then find the angle between vecb and vecc .