Home
Class 12
MATHS
If vectors hati-2xhatj-3yhatk and hati+ ...

If vectors `hati-2xhatj-3yhatk and hati+ 3 x hatj + 2yhatk` are orthogonal to each other, then find the locus of th point (x,y).

Text Solution

Verified by Experts

It is given that vectors `hati - 2xhatj - 3yhatk and hati + 3x hatj + 2yhatk` are orthogonal , therefore,
`(hati-2xhatj - 3yhatk).(hati+3xhatj+2yhatk)=0`
` or 1-6x^(2)-6y^(2)=0`
`or bx^(2)+6y^(2)=1` whiche is a circle.
Promotional Banner

Topper's Solved these Questions

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Exercise 2.2|15 Videos

  • 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 Multiple correct answers type|11 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 the vectors 3 hati - 2hatj + mhatk and -2 hati + hatj + 4 hatk are perpendicular to each other, find the value of m.

veca = 3hati + 3hatj - hatk and vecb = 2hati + 6hatj + mhatk are perpendicular to each other , then the value of m is

If the vectors veca= 3x hati+4y hatj-12hatk and vecb=3x hati-4y hatj+12hatk are mutually perpendicular, then the locus of the point (x, y) is a/an -

If veca = xhati +2 hatj-zhatk and vecb = 3hati -y hatj+hatk are two equal vecots then find the value of x+y+z

If 2hati - 3hatj-hatk & ahati + bhatj- 2hatk these two vectors are parallel to each other. Then find out the value of b.

Show that the vectors 2hati-3hatj+4hatkand-4hati+6hatj-8hatk are collinear.

vecA =2hati+3hatj+4hatk and vecB=hati-hatj+hatk are two vectors. Find vecAxxvecB .

Find the angle between the vectors hati-2hatj+3hatkand3hati-2hatj+hatk

vecA =2hati +3hatj+4hatk & vecB=hati- hatj + hatk are two given vectors. Find out the value of barA xx barB .

CENGAGE PUBLICATION-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise 2.1
  1. Find |veca|and |vecb|, if (veca+vecb).(veca-vecb) =8 and |veca|=8|vecb...

    Text Solution

    |

  2. Show that | vec a| vec b+| vec b| vec a is a perpendicular to | vec a|...

    Text Solution

    |

  3. If the vectors A ,B ,C of a triangle A B C are (1,2,3),(-1,0,0),(0,1,2...

    Text Solution

    |

  4. If |a|=3,|b|=4a n d the angle between aa n db is 120^0 , then find the...

    Text Solution

    |

  5. If vectors hati-2xhatj-3yhatk and hati+ 3 x hatj + 2yhatk are orthogon...

    Text Solution

    |

  6. Let veca ,vecb and vecc be pairwise mutually perpendicular vectors, su...

    Text Solution

    |

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

    Text Solution

    |

  8. If the angle between unit vectors veca and vecb is 120^(@) . Then find...

    Text Solution

    |

  9. Let vecu=hati+hatj,vecv=hati-hatj and vecw=hati+2hatj+3hatk. If hatn i...

    Text Solution

    |

  10. A , B , C , D are any four points, prove that vec A Bdot vec C D+ v...

    Text Solution

    |

  11. P(1,0,-1), Q(2,0,-3),R(-1,2,0)a n dS(3,-2,-1), then find the projectio...

    Text Solution

    |

  12. If the vectors 3 vec p+ vec q ;5p-3 vec qa n d2 vec p+ vec q ;3 vec p-...

    Text Solution

    |

  13. Let vec A and vec B be two non-parallel unit vectors in a plane. If...

    Text Solution

    |

  14. Let vec a , vec ba n d vec c be unit vectors, such that vec a+ vec b...

    Text Solution

    |

  15. If veca and vecb are unit vectors, then find the greatest value of |ve...

    Text Solution

    |

  16. Constant forces P1= hat i+ hat j+ hat k ,P2= - hat i+2 hat j- hat ka n...

    Text Solution

    |

  17. Find |veca|and |vecb|, if (veca+vecb).(veca-vecb) =8 and |veca|=8|vecb...

    Text Solution

    |

  18. If A ,B ,C ,D are four distinct point in space such that vec(A B) is...

    Text Solution

    |