Home
Class 12
MATHS
If the vector product of a constant vect...

If the vector product of a constant vector ` vec O A` with a variable vector ` vec O B` in a fixed plane `O A B` be a constant vector, then the locus of `B` is a. a straight line perpendicular to ` vec O A` b. a circle with centre `O` and radius equal to `| vec O A|` c. a straight line parallel to ` vec O A` d. none of these

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC RATIOS FOR COMPOUND, MULTIPLE, SUB-MULTIPLE ANGLES, AND TRANSFORMATION FORMULAS

    CENGAGE ENGLISH|Exercise Multiple Correct Answers Type|6 Videos
  • VECTORS TRIPLE PRODUCTS, RECIPROCAL SYSTEM OF VECTORS

    CENGAGE ENGLISH|Exercise DPP 2.4|20 Videos

Similar Questions

Explore conceptually related problems

If a vector vec a is perpendicular to two non-collinear vector vec b and vec c , then vec a is perpendicular to every vector in the plane of vec b and vec c .

If a vector vec(A) is parallel to another vector vec(B) then the resultant of the vector vec(A)xxvec(B) will be equal to

Let vec a= hat i be a vector which makes an angle of 120^@ with a unit vector vec b in XY plane. then the unit vector (vec a+ vec b) is

If a vector vec a is perpendicular to two non collinear vectors vec b\ a n d\ vec c ,\ t h e n\ \ vec a\ is perpendicular to every vector in the plane of \ vec b\ a n d\ vec c

The vector component of vec b perpendicular to vec a is a. ( vec bdot vec c) vec a b. ( vec axx( vec bxx vec a))/(| vec a|^2) c. vec axx( vec bxx vec a) d. none of these

If vec c is a unit vector perpendicular to the vectors vec a\ a n d\ vec b write another unit vector perpendicular vec a\ a n d\ vec bdot

If vec a , vec b are two vectors such that | vec a+ vec b|=| vec b|, then prove that vec a+2 vec b is perpendicular to vec a .

If vec a\ a n d\ vec b are mutually perpendicular unit vectors, write the value of | vec a+ vec b|dot

The resultant and dot product of two vectors vec(a) and vec(b) is equal to the magnitude of vec(a) . Show that when the vector vec(a) is doubled , the new resultant is perpendicular to vec(b) .

A vector vec r is inclined at equal to O X ,O Ya n dO Zdot If the magnitude of vec r is 6 units, find vec rdot

CENGAGE ENGLISH-VECTOR ALGEBRA-All Questions
  1. If vec a and vec b are any two vectors of magnitudes 2 and 3, respe...

    Text Solution

    |

  2. If vec a\ a n d\ vec b are two vectors such that | vec axx vec b|=3\...

    Text Solution

    |

  3. If the vector product of a constant vector vec O A with a variable ve...

    Text Solution

    |

  4. Let vec u , vec va n d vec w be such that | vec u|=1,| vec v|=2a n d|...

    Text Solution

    |

  5. If the two adjacent sides of two rectangles are represented by vecto...

    Text Solution

    |

  6. Let P ,Q ,R and S be the points on the plane with position vectors ...

    Text Solution

    |

  7. vec u , vec v and vec w are three non-coplanar unit vecrtors and alp...

    Text Solution

    |

  8. If vec a=a1 hat i+a2 hat j+a3 hat k ; vec b=b1 hat i+b2 hat j+b3 hat...

    Text Solution

    |

  9. Find the absolute value of parameter t for which the area of the ...

    Text Solution

    |

  10. The condition for equations vec rxx vec a= vec ba n d vec rxx vec c...

    Text Solution

    |

  11. If aa n db are nonzero non-collinear vectors, then [ vec a vec b hat...

    Text Solution

    |

  12. ( vec a+ vec b)dot( vec b+ vec c)xx( vec a+ vec b+ vec c)= [ vec a\ ...

    Text Solution

    |

  13. A vector of magnitude 10 along the normal to the curve 3x^2+8x y+2y^2-...

    Text Solution

    |

  14. If a( vecalphaxx vecbeta)+b( vecbetaxx vecgamma)+c( vecgammaxx vecalph...

    Text Solution

    |

  15. If ( vec axx vec b)xx( vec bxx vec c)= vec b ,w h e r e vec a , vec b ...

    Text Solution

    |

  16. If vec a , vec b , vec c are any three noncoplanar vector, then ( ...

    Text Solution

    |

  17. If vec x+ vec cxx vec y= vec aa n d vec y+ vec cxx vec x= vec b ,w h ...

    Text Solution

    |

  18. If vec aa n d vec b are two unit vectors incline at angle pi//3 , ...

    Text Solution

    |

  19. If vec a and vec b are orthogonal unit vectors, then for a vector ...

    Text Solution

    |

  20. Let V be the volume of the parallelepiped formed by the vectors vec a ...

    Text Solution

    |