Home
Class 11
PHYSICS
If vecb and vec c be the intersecting fa...

If `vecb` and `vec c` be the intersecting face-diagonals of a cube of edge a in the planes XOY and YOZ respectively with respect to a frame of reference erected at the point of intersection of the vectors and edges of the cube as the axes, find (a) the components of the vector `vecd`, where `vecd=vecbxxvec c` and (b) the values of `vecb.vec c` and `vecd.vec c`.

Text Solution

Verified by Experts

The correct Answer is:
(a)`d_x=d_z=a^2, d_y=-a^2` , (b)`vecb.vec c=a^2, vecd.vec c=0`
Promotional Banner

Topper's Solved these Questions

  • UNITS AND DIMENSION

    NN GHOSH|Exercise EXERCISE|26 Videos

  • VELOCITY OF SOUND

    NN GHOSH|Exercise EXERCISE|26 Videos

Similar Questions

Explore conceptually related problems

If vec a,vec b, and vec c are unit vectors such that vec a+vec b+vec c=0, then find the value of vec a*vec b+vec b*vec c+vec c*vec a

For any three vectors vec a;vec b;vec c find [vec a+vec b;vec b+vec c;vec c+vec a]

If vec(b) and vec(c) are the position vectors of the points B and C respectively, then the position vector of the point D such that vec(BD) = 4 vec(BC) is

If vec(b) and vec(c ) are the position vectors of the points B and C respectively, then the position vector of the point D such that vec(BD)= 4 vec(BC) is

Find the point of intersection of the three planes vec r*vec a=1,vec r*vec b=1,vec r*vec c=1 where vec a,vec b,vec c are three non coplaner vector.

If vec a, vecb and vec c are three conterminuous edges of a parallelopiped of the volume 6 then find the value of [[vec a xx vec b, vec a xx vec c, vec b xx vec c]] .

vec a,vec b and vec c are the position vectors of points A,B and C respectively,prove that: vec a_(vec a)xvec b+vec bxvec c+vec cxvec a is vector perpendicular to the plane of triangle ABC.

If veca,vecb,vecc,vecd be the position vectors of points A,B,C,D respectively and vecb-veca=2(vecd-vecc) show that the pointf intersection of the straighat lines AD and BC divides these line segments in the ratio 2:1.

Let veca=hat i-2 hat j+hat k, vecb=hat i-hat j+hat k and vec c is nonzero vector and vecb xx vec c= vec b xx vec a, vec a.vec c=0 . Find vecb.vec c .

NN GHOSH-VECTOR AND SCALARS-All Questions
  1. Show that veca.(vecbxxvec c) is equal in magnitude to the volume of th...

    Text Solution

    |

  2. Prove that for a vector veca defined by veca=axveci+ayvecj+azveck, the...

    Text Solution

    |

  3. If vecb and vec c be the intersecting face-diagonals of a cube of edge...

    Text Solution

    |

  4. Show that the position vector of a place on the surface of the earth w...

    Text Solution

    |

  5. A man rows a boat with a speed 10 m/s along N-E direction. The shore l...

    Text Solution

    |

  6. A force vecF=5veci+2vecj+veck displaces a body from a point with coord...

    Text Solution

    |

  7. If the sum and difference of two vectors are at right angles, show tha...

    Text Solution

    |

  8. Prove that (vecaxxvecb)^2=veca^2b^2-(veca.vecb)^2.

    Text Solution

    |

  9. Show that if two vectors are equal in magnitude, their vector sum and ...

    Text Solution

    |

  10. Find the area of the parallelogram whose sides are represented by 2h...

    Text Solution

    |

  11. Show that (veca+vecb)xx(veca-vecb)=-2(vecaxxvecb) and use this result ...

    Text Solution

    |

  12. Find the equation of a line through a point C of position vector vec c...

    Text Solution

    |

  13. Find the moment of a force , vecF=3veci+2vecj acting at point vecr=vec...

    Text Solution

    |

  14. If vecP+vecQ=vecR and vecP-vecQ=vecS, prove that vecR^2+vecS^2=2(vecP^...

    Text Solution

    |

  15. Show that a vector remains invariant (unchanged ) under rotation of co...

    Text Solution

    |

  16. Find the components of a vector vecA=2hati+3hatj along the directions ...

    Text Solution

    |

  17. The force on a positively charged particle is given by vecF=qvecE+qvec...

    Text Solution

    |

  18. A point P lies on a vector veca.the position vector of the point is ve...

    Text Solution

    |

  19. Show that if vecu.(dvecu)/(dt)=0 the vector vecu is of constant magnit...

    Text Solution

    |

  20. If veca=m vecb+vec c, find the scalar m.

    Text Solution

    |