Home
Class 12
MATHS
Find the value of x for which x( hat i+...

Find the value of x for which `x( hat i+ hat j+ hat k)`is a unit vector.

Text Solution

Verified by Experts

The correct Answer is:
`= pm (1)/(sqrt(3))`.
Promotional Banner

Topper's Solved these Questions

  • VECTOR ALGEBRA

    MODERN PUBLICATION|Exercise Exercise|3 Videos
  • VECTOR ALGEBRA

    MODERN PUBLICATION|Exercise Revision Exercise|10 Videos
  • VECTOR ALGEBRA

    MODERN PUBLICATION|Exercise Ncert File Question from Ncert Book (Exercise 10.5)|7 Videos
  • THREE DIMENSIONAL GEOMETRY

    MODERN PUBLICATION|Exercise CHAPTER TEST 11|11 Videos

Similar Questions

Explore conceptually related problems

Find the values of 'x' for which x(hat(i)+hat(j)+hat(k)) is a unit vector.

Find the value of a for which the vector 3 hat i + 3 hat j + 9 hat k and hat i + a hat j + 3 hat k are parallel.

The vector (hat i +hat j) is a unit vector.

For what value of p, is (hat i+hat j+hat k)p a unit vector?

The position vector of a point is R =x hat i +y hat j + z hat k and another vector is A =3 hat i +2 hat j + 5hat k .Which of the mathematical relations is correct ?

Find the value of x and y if the vectors vec a=3hat i+xhat j-hat k and vec b=2hat i+hat j+yhat k are mutually perpendicular vectors of equal magnitude.

Find the values of a for which are vectors vecalpha= hat i+2 hat j+ hat k , vecbeta=a hat i+ hat j+2 hat k\ a n d\ vecgamma= hat i+2 hat j+a hat k are coplanar. \

What is the value of lamda for which the vectors hat(i) - hat(j) + hat(k), 2hat(i) + hat(j)- hat(k) and lamda hat(i) - hat(j)+ lamda (k) are coplanar

Find the values of x and y if the vectors vec a=3hat i+xhat j-hat k and vec b=2hat i+hat j+yhat k are mutually perpendicular vectors of equal magnitude.

Find the value of lambda for which the four points with position vectors (-hat(j)+hat(k)), (2hat(i)-hat(j)-hat(k)), (hat(i)+lambda hat(j)+hat(k))and (3hat(j)+3hat(k)) are coplanar.

MODERN PUBLICATION-VECTOR ALGEBRA -Miscellaneous Exercise on Chapter 10
  1. Write down a unit vector in XY-plane, making an angle of 30 with th...

    Text Solution

    |

  2. Find the scalar components and magnitude of the vector joining the po...

    Text Solution

    |

  3. A girl walks 4 km towards west, then she walks 3 km in a direction 30...

    Text Solution

    |

  4. If vec(a)=vec(b)+vec(c ), then is it true that |vec(a)|=|vec(b)|+|vec(...

    Text Solution

    |

  5. Find the value of x for which x( hat i+ hat j+ hat k)is a unit vector...

    Text Solution

    |

  6. Find a vector of magnitude 5 units, and parallel to the resultant of ...

    Text Solution

    |

  7. If -> a= hat i+ hat j+ hat k , -> b=2 hat i- hat j+3 hat k and -...

    Text Solution

    |

  8. Show that the points A(1, -2, -8), B(5, 0, -2) and C(11, 3, 7) are col...

    Text Solution

    |

  9. Find the position vector of a point R which divides the line joinin...

    Text Solution

    |

  10. The two adjacent sides of a parallelogram are 2 hat i-4 hat j+5 hat k ...

    Text Solution

    |

  11. Show that the direction cosines of a vector equally inclined to the a...

    Text Solution

    |

  12. Let -> a= hat i+4 hat j+2 hat k , -> b=3 hat i-2 hat j+7 hat k and...

    Text Solution

    |

  13. The scalar product of the vector hat i+ hat j+ hat kwith a unit vect...

    Text Solution

    |

  14. If vec a , vec b , vec c are mutually perpenedicular vectors of eq...

    Text Solution

    |

  15. Prove that ( -> a+ -> b)dot( -> a+ -> c)| -> a|^2+| -> b|^2 , if and o...

    Text Solution

    |

  16. If theta is the angle between two vectors vec a\ a n d\ vec b ,\ t h...

    Text Solution

    |

  17. If vec a\ a n d\ vec b be two unit vectors and theta is the angle be...

    Text Solution

    |

  18. Write the value of hat(i).(hat(j)xxhat(k))+hat(j).(hat(i)xxhat(k))+ha...

    Text Solution

    |

  19. If is the angle between any two vectors -> a and -> b , then ...

    Text Solution

    |