Home
Class 12
MATHS
If a unit vector vec a makes angle pi//...

If a unit vector ` vec a` makes angle `pi//3` with ` hat i ,pi//4` with ` hat j` and an acute angle `theta` with ` hat k` , then find the components of ` vec a` and the angle `thetadot`

A

`(5pi)/6`

B

`pi/4`

C

`(5pi)/12`

D

`(2pi)/3`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • VECTORS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED (ARCHIVE)|36 Videos

  • VECTORS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED (ARCHIVE) (INTEGER TYPE)|4 Videos

  • VECTORS

    VMC MODULES ENGLISH|Exercise Numerical ValueType for JEE Main|15 Videos

  • TRIGONOMETRIC IDENTITIES AND EQUATIONS

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|11 Videos

Similar Questions

Explore conceptually related problems

If a unit vector vec a makes an angle pi/3 with hat i ,\ pi/4 with hat j and an acute angle theta with hat k then find theta and hence, the components of vec a .

If a unit vector vec a makes angles pi/3 with hat i ,pi/4 with hat j and an acute angle theta with hat k , then find the value of theta .

If a unit vector vec(a) makes a angle (pi)/(3) with hat(i), (pi)/(4) with hat(k) and an acute angle q with hat(j) then find the value of q.

A unit vector vec a makes angles pi/4\ a n d\ pi/3 with hat i\ a n d\ hat j respectively and an acute angle theta with hat kdot Find the angle theta and components of vec adot

A unit vector vec r makes angle pi/3\ a n d\ pi/2 with hat j a n d\ hat k respectively and an acute angle theta\ w i t h\ i , Find thetadot

If a unit vector vec(a) makes angle (pi)/(3) with hat(i), (pi)/(4) with hat(j) and theta in ((pi)/(2), pi) with hat(k) then a value of theta is (k pi)/(l) (k and l are coprime). The value of k is _________.

In sub-parts (i) and (ii) choose the correct option and in sub-parts (iii) to (v), answer the questions as instructed. If a unit vector hat(a) makes angle pi/3 with hat(i), pi/3" with " hat(j) and an acute angle theta with k, then find theta .

If vec a.hat i= vec a.( hat i+ hat j)= vec a.( hat i+ hat j+ hat k) , then find the unit vector vec a

Find a unit vector in XY plane, which makes an angle of 45^@ with the vector hat i +hat j and an angle of 60^@ with the vector 3hat i – 4hat j .

If vec a=x hat i+(x-1) hat j+ hat k and vec b=(x+1) hat i+ hat j+a hat k make an acute angle AAx in R , then find the values of adot

VMC MODULES ENGLISH-VECTORS -JEE MAIN (ARCHIVE)
  1. Let veca,vecb and vecc be non-zero vectors such that no two are collin...

    Text Solution

    |

  2. A tetrahedron has vertices O (0,0,0), A(1,2,1,), B(2,1,3) and C(-1,1,2...

    Text Solution

    |

  3. If |(a,a^2,1+a^3),(b,b^2,1+b^3),(c,c^2,1+c^2)|=0 and vectors (1,a,a^2)...

    Text Solution

    |

  4. If vecu,vecv and vecw are three non coplanar vectors then (vecu+vecv-v...

    Text Solution

    |

  5. Consider points A,B,C annd D with position vectors 7hati-4hatj+7hatk,h...

    Text Solution

    |

  6. Let A(3,0,-1), B(2,10,6) and C(1,2,1) be the vertices of a triangle an...

    Text Solution

    |

  7. If a unit vector vec a makes angle pi//3 with hat i ,pi//4 with hat...

    Text Solution

    |

  8. Let a=hati + hatj + sqrt(2)hatk, b=b(1)hati + b(2)hatj + sqrt(2)hatk a...

    Text Solution

    |

  9. Prove that the line x=ay+b, z=cy+d and x=a'y+b', z=dy+d' are perpendic...

    Text Solution

    |

  10. Let a=3hati + 2hatj + 2hatk and b= hati + 2hatj - 2hatk be two vectors...

    Text Solution

    |

  11. Let alpha epsilon R and the three vectors veca=alpha hati+hatj+3hatk, ...

    Text Solution

    |

  12. If the length of the perpendicular from the point (beta, 0,beta) (beta...

    Text Solution

    |

  13. Let vecalpha = 3hati + hatj and beta= 2hati - hatj + 3hatk. If vecbeta...

    Text Solution

    |

  14. Let a=3hati + 2hatj + xhatk and b = hati - hatj + hatk, for some real ...

    Text Solution

    |

  15. The sum of the distinct real values of mu, for which the vectors, mu h...

    Text Solution

    |

  16. If veca=hati+2hatj+4hatk, vecb=hati+lamdahatj+4hatk, vecc=2hati+4hatj+...

    Text Solution

    |

  17. Let a=hati - hatj, b=hati + hatj + hatk and c be a vector such that a ...

    Text Solution

    |

  18. Let a , b and c be three unit vectors out of which vectors b an...

    Text Solution

    |

  19. Let alpha = (lambda-2) a + b and beta =(4lambda -2)a + 3b be two given...

    Text Solution

    |

  20. Let veca = 2hati+lambda1 hatj+3hatk, vec(b)=4hati+(3-lambda2) hatj+6ha...

    Text Solution

    |