Home
Class 14
MATHS
If x hat(i) + y hat(j) + z hat(k) is a u...

If `x hat(i) + y hat(j) + z hat(k)` is a unit vector and `x:y:z= sqrt3:2:3` then what is the value of z?

A

`(3)/(16)`

B

3

C

`(3)/(4)`

D

2

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • VECTOR

    PUNEET DOGRA|Exercise Prev Year Questions|134 Videos

  • TRIGONOMETRY

    PUNEET DOGRA|Exercise PREV YEAR QUESTIONS|163 Videos

Similar Questions

Explore conceptually related problems

If x hat(i)+ y hat(j)+zhat(k) is a unit vector and x:y:z=sqrt(3):2:3 , then what is the value of z?

The vectors hat(i)- x hat(j)- y k and hat(i) + x hat(j) + y hat(k) are orthogonal to reach other, then what is the locus of the point (x,y)?

If hat(i), hat(j) and hat(k) are unit vectors along x,y and z-axis respectively, the angle theta between the vector hat(i) + hat(j) + hat(k)" ""and vector" hat(j) is given by

If hat(i), hat(j) and hat(k) represent unit vectors along the x, y and z axes respectively, then the angle theta between the vectors (hat(i) + hat(j) + hat(k)) and (hat(i) + hat(j)) is equal to :

If vec(r )= x hat(i) + y hat(j) + z hat(k) , then what is vec(r ). (hat(i ) + hat(j) + hat(k)) equal to?

What is the value of b such that the scalar product of the vector hat(i) + hat(j) + hat(k) with the unit vector parallel to the sum of the vectors 2hat(i) + 4hat(j)-5hat(k) and b hat(i) + 2hat(j) + 3hat(k) is unity ?

Let overset(to)(a_(r))=x_(r )hat(i)+y_(r )hat(j)+z_(r )hat(k),r=1,2,3 three mutually prependicular unit vectors then the value of |{:(x_(1),,-x_(2),,x_(3)),(y_(1),,y_(2) ,,y_(3)),(z_(1),,z_(2),,z_(3)):}| is equal to

If the vectors hat(i)-x hat(j)-y hat(k) and hat(i)+x hat(j)+y hat(k) are orthogonal to each other, then what is the locus of the point (x, y) ?

If the vectors -hat(i)-2xhat(j)-3y hat(k) and hat(i)-3x hat(j)-2y hat(k) are orthogonal to each other, then what is the locus of the point (x, y) ?

If vector hat(i) - 3hat(j) + 5hat(k) and hat(i) - 3 hat(j) - a hat(k) are equal vectors, then the value of a is :

PUNEET DOGRA-VECTOR-Prev Year Questions
  1. For what value of m are the point with position vectors, 10 hat(i) + 3...

    Text Solution

    |

  2. For what value of m are the vector 2hat(i) - 3hat(j) + 4hat(k), hat(i)...

    Text Solution

    |

  3. If x hat(i) + y hat(j) + z hat(k) is a unit vector and x:y:z= sqrt3:2:...

    Text Solution

    |

  4. What is the projection of the vector hat(i)-2 hat(j) + hat(k) on the v...

    Text Solution

    |

  5. If the vector vec(a) lies in the planar of vectors vec(b) and vec(c ),...

    Text Solution

    |

  6. What is the sine of the angle between the vectors hat(i) + 2hat(j) + 3...

    Text Solution

    |

  7. If p, q, r and s be respectively the magnitude of the vectors 3hat(i)-...

    Text Solution

    |

  8. Which one of the following is the unit vector perpendicular to the vec...

    Text Solution

    |

  9. Consider the following statements in respect of the vectors vec(u)(1)=...

    Text Solution

    |

  10. If the position vector of a point p with respect to the origin O is ha...

    Text Solution

    |

  11. ABCD is a quadrilateral. Force vec(AB), vec(CB), vec(CD) and vec(DA) a...

    Text Solution

    |

  12. PQRS is a parallelogram, where vec(PQ) = 3hat(i) + 2hat(j) - m hat(k) ...

    Text Solution

    |

  13. What is the value of b such that the scalar product of the vector hat(...

    Text Solution

    |

  14. Let a, b and c b the distinct non-negative numbers. If the vectors a h...

    Text Solution

    |

  15. What is the vector equally inclined to the vectors hat(i)+ 3hat(j) and...

    Text Solution

    |

  16. Find the area of the triangle whose vertices are A(3, -1,2) ,B(1, - 1,...

    Text Solution

    |

  17. If   vec(a) = hat(i)- hat(k) , vec(b) = x hat(i) + hat(j) + (1-x) hat(...

    Text Solution

    |

  18. Consider the following statements 1. For any three vectors vec(a) ve...

    Text Solution

    |

  19. The vectors vec(a)= x hat(i) + z hat(k), vec(b) = hat(k), vec(c ) are ...

    Text Solution

    |

  20. Let vec(a) and vec(b) be two unit vectors and α be the angle between ...

    Text Solution

    |