Home
Class 12
MATHS
Determine the sine of the angle between ...

Determine the sine of the angle between the vectors `5hati-3hatj, 3hati-2hatk`

Text Solution

Verified by Experts


`|vecaxxvecb| = sqrt(36+100+81) = sqrt(217)`
`|veca| = sqrt(25+9) = sqrt(34)`
`|vecb| = sqrt(9+4) = sqrt(13)`
If `theta` is the angle between `veca` and `vecb` then
`sintheta = |vecaxxvecb|/(|veca||vecb| = sqrt(217)/(sqrt(34) sqrt(13)) = sqrt((217)/442).
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    MBD PUBLICATION|Exercise QUESTION BANK|267 Videos

Similar Questions

Explore conceptually related problems

Determine the sine of the angle between the vectors hat-3hatj+hatk, hati+hatj+hatk

Find the angle between the vectors 3hati+ 4hatj and 2hati+hatj+hatk .

Find sine of the angle between the vectors vecA=hati+2hatj+3hatk and vecB=2hati-hatj+hatk

Find the angle between the vectors 3hati + 4hatj and 2hati+hatj+sqrt3hatk

Find the unit vectors perpendicular to the vectors. hati+hatj , hati-hatk

Find the angle between the vectors vecp=3hati+hatj+2hatk and vecQ=hati-2hatj+3hatk .

What is the angle between hati+ hatj and hati-hatj ?

Find the unit vectors perpendicular to the vectors. 2hati+3hatk , hati-2hatj

Determine the area of the parallelogram whose sides are the vectors 2hati + 2hatj and hati -hatk .

Find the volume of the parallelopiped whose sides are given by the vectors. hati+hatj+hatk, hatk, 3hati-hatj+2hatk.

MBD PUBLICATION-VECTORS-QUESTION BANK
  1. Calculate the area of the triangle ABC (by vector method) where A(1,2,...

    Text Solution

    |

  2. Calculate the area of the triangle ABC (by vector method) where A(1,1,...

    Text Solution

    |

  3. Determine the sine of the angle between the vectors 5hati-3hatj, 3hati...

    Text Solution

    |

  4. Determine the sine of the angle between the vectors hat-3hatj+hatk, ha...

    Text Solution

    |

  5. Show that (vecaxxvecb)^2 = a^2b^2 - (veca.vecb)^2.

    Text Solution

    |

  6. If vecaxxvecb = vecbxxvecc ne vec0, prove that veca+vecc = mvecb, wher...

    Text Solution

    |

  7. if vec = 2hati+hatj-hatk, vecb = -hati+2hatj-4hatk, vecc = hati+hatj+h...

    Text Solution

    |

  8. If veca = 3hati+hatj-2hatk, vecb = 2hati-3hatj+4hatk then verify that ...

    Text Solution

    |

  9. Find the area of the parallelogram whose diagonals are vectors 3hati+h...

    Text Solution

    |

  10. Show that (veca-vecb)xx(veca+vecb) = 2(vecaxxvecb). Interpret this res...

    Text Solution

    |

  11. Each question given below has four possible answers out of which only ...

    Text Solution

    |

  12. (-veca).vecbxx(-vecc)) =

    Text Solution

    |

  13. For the non-zero vectors veca, vecb and vecc, veca.(vecbxxvecc) = 0 if

    Text Solution

    |

  14. Find the scalar triple product vecb.(veccxxveca) where veca, vecb and ...

    Text Solution

    |

  15. Find the scalar triple product vecb.(veccxxveca) where veca, vecb and ...

    Text Solution

    |

  16. Find the volume of the parallelopiped whose sides are given by the vec...

    Text Solution

    |

  17. Find the volume of the Parallelepiped whose sides are given by the vec...

    Text Solution

    |

  18. Show that the following vector are co-planar. hati-2hatj+2hatk, 3hati+...

    Text Solution

    |

  19. Show that the following vector are co-planar. hati+2hatj+3hatk, -2hati...

    Text Solution

    |

  20. Find the value of lambda so that the three vectors are co-planar. hati...

    Text Solution

    |