Home
Class 12
MATHS
Find a unit vector in XY plane which mak...

Find a unit vector in XY plane which makes an angle `45^(@)` with the vector `hati + hatj` at angle of `60^(@)` with the vector `3 hati - 4 hatj.`

Text Solution

Verified by Experts

The correct Answer is:
`(13)/(sqrt(170)) hati + (1)/(sqrt (170))hatj`
Promotional Banner

Topper's Solved these Questions

  • VECTORS

    CBSE COMPLEMENTARY MATERIAL|Exercise TWO MARKS QUESTIONS|11 Videos

  • THREE DIMENSIONAL GEOMETRY

    CBSE COMPLEMENTARY MATERIAL|Exercise SIX MARK QUESTIONS|9 Videos

Similar Questions

Explore conceptually related problems

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 i4hat j

Find the unit vector which makes an angle of 45^(@) with the vector 2hati+2hatj-hatk and an angle of 60^(@) with the vector hatj-hatk .

A unit vector in xy-plane that makes an angle of 45^0 with the vector hati+hatj and angle of 60^0 with the vector 3hati-4hatj is (A) hati (B) (hati+hatj)/sqrt(2) (C) (hati-hatj)/sqrt(2) (D) none of these

Unit vector in the xyplane that makes and angle of 45^0 with the vector hati+hatj and an angle of 60^0 with the vector 3hati-4hatj is (A) hati (B) (hati+hatj)/sqrt(2) (C) (hati-hatj)/sqrt(2) (D) none of these

The vector veca=1/4(2hati-2hatj+hatk) (A) is a unit vector (B) makes an angle of pi/3 with the vector (hati+1/2 hatj-hatk) (C) is parallel to the vector 7/4hati-7/4hatj+7/8hatk (D) none of these

CBSE COMPLEMENTARY MATERIAL-VECTORS -FOUR MARKS QUESTIONS
  1. Prove that the four points (4hati + 5 hatj+hatk), - (hatj +hatk),(3hat...

    Text Solution

    |

  2. If |veca| =3, |vecb|=4 and |vecc|=5 such that each is perpendicular to...

    Text Solution

    |

  3. Decompose the vector 6 hati - 3 hatj - 6 hatk into vectors which are p...

    Text Solution

    |

  4. If veca, vecb and vecc are vectors such that veca. vecb = veca.vecc, v...

    Text Solution

    |

  5. If veca, vecb and vecc are three non zero vectors such that veca xx v...

    Text Solution

    |

  6. For any three vectors veca, vecb, vecc the value of [(veca-vecb, vecb-...

    Text Solution

    |

  7. If [veca vecbvecc]=2 find the volume of the parallelepiped whose co-te...

    Text Solution

    |

  8. If veca +vecb +vecc=0, |veca|=3,|vecb|=5, |vecc|=7 , then find the ang...

    Text Solution

    |

  9. If the magnitude of the vector product of the vector hati+hatj+hatk wi...

    Text Solution

    |

  10. If vecaxxvecb=veccxxvecd and vecaxxvecc=vecbxxvecd show that (veca-vec...

    Text Solution

    |

  11. Find a vector of magnittude sqrt(171) which is perpendicular to both o...

    Text Solution

    |

  12. If a is a nonzero real number prove that the vectors overset(r) alph...

    Text Solution

    |

  13. If with reference to a right handed system of mutually perpendicula...

    Text Solution

    |

  14. Find a unit vector perpendicular to plane ABC when position vectors of...

    Text Solution

    |

  15. Find a unit vector in XY plane which makes an angle 45^(@) with the ve...

    Text Solution

    |

  16. Suppose veca = lamda hati - 7 hatj + 3 hatk, vecb = lamda hati + hatj ...

    Text Solution

    |

  17. Let vecV = 2hati +hatj - hatk and vecW= hati + 3hatk . if vecU is a u...

    Text Solution

    |

  18. Let veca=hati-hatk, vecb=xhati+hatj+(1-x)hatk and vecc=yhati+xhatj+(1+...

    Text Solution

    |

  19. Let a, b and c be distinct non-negative numbers. If vectos a hati +a h...

    Text Solution

    |

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

    Text Solution

    |