Home
Class 12
MATHS
If vec a , vec b and vec c are three n...

If ` vec a , vec b` and ` vec c` are three non-zero, non coplanar vector ` vec b_1= vec b-( vec bdot vec a)/(| vec a|^2) vec a` , ` vec c_1= vec c-( vec cdot vec a)/(| vec a|^2) vec a+( vec bdot vec c)/(| vec c|^2) vec b_1` , `, c_2= vec c-( vec cdot vec a)/(| vec a|^2) vec a-( vec bdot vec c)/(| vec b_1|^2)` , `b_1, vec c_3= vec c-( vec cdot vec a)/(| vec c|^2) vec a+( vec bdot vec c)/(| vec c|^2) vec b_1` , ` vec c_4= vec c-( vec cdot vec a)/(| vec c|^2) vec a=( vec bdot vec c)/(| vec b|^2) vec b_1` then the set of orthogonal vectors is `( vec a , vec b_1, vec c_3)` b. `( vec a , vec b_1, vec c_2)` c. `( vec a , vec b_1, vec c_1)` d. `( vec a , vec b_2, vec c_2)`

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 vec a , vec b , vec c are three non-coplanar vectors, prove that [ vec a+ vec b+ vec c vec a+ vec b vec a+ vec c]=-[ vec a vec b vec c]

If vec a , vec ba n d vec c are three non coplanar vectors, then prove that vec d=( vec a.vec d)/([ vec a vec b vec c])( vec bxx vec c)+( vec b.vec d)/([ vec a vec b vec c])( vec cxx vec a)+( vec c. vec d)/([ vec a vec b vec c])( vec axx vec b)

If vec a , vec b and vec c are three non-coplanar vectors, then ( vec a+ vec b+ vec c).[( vec a+ vec b)xx( vec a+ vec c)] equals a. 0 b. [ vec a vec b vec c] c. 2[ vec a vec b vec c] d. -[ vec a vec b vec c]

If vec adot vec b=betaa n d vec axx vec b= vec c ,t h e n vec b is ((beta vec a- vec axx vec c))/(| vec a|^2) b. ((beta vec a+ vec axx vec c))/(| vec a|^2) c. ((beta vec c- vec axx vec c))/(| vec a|^2) d. ((beta vec a+ vec axx vec c))/(| vec a|^2)

If vec a is perpendicular to vec b and vec r is non-zero vector such that p vec r+( vec rdot vec a) vec b= vec c , then vec r= vec c/p-(( vec adot vec c) vec b)/(p^2) (b) vec a/p-(( vec cdot vec b) vec a)/(p^2) vec a/p-(( vec adot vec b) vec c)/(p^2) (d) vec c/(p^2)-(( vec adot vec c) vec b)/p

If vec a , vec b ,a n d vec c are three non-coplanar non-zero vecrtors, then prove that ( vec a . vec a) vec bxx vec c+( vec a . vec b) vec cxx vec a+( vec a . vec c) vec axx vec b=[ vec b vec c vec a] vec a

If vec a ,\ vec b ,\ vec c are three non coplanar vectors, then ( vec a+ vec b+ vec c)dot[( vec a+ vec b)xx) vec a+ vec c)] equals [ vec a\ vec b\ vec c] b. "\ "0"\ " c. 2[ vec a\ vec b\ vec c] d. -[ vec a\ vec b\ vec c]

For any three vectors vec a , vec b , vec c , prove that | vec a+ vec b+ vec c|^2=| vec a|^2+| vec b|^2+| vec c|^2+2( vec adot vec b+ vec bdot vec c+ vec cdot vec a)

If vec a , vec ba n d vec c are three mutually perpendicular vectors, then the vector which is equally inclined to these vectors is a. vec a+ vec b+ vec c b. vec a/(| vec a|)+ vec b/(| vec b|)+ vec c/(| vec c|) c. vec a/(| vec a|^2)+ vec b/(| vec b|^2)+ vec c/(| vec c|^2) d. | vec a| vec a-| vec b| vec b+| vec c| vec c

If non-zero vectors vec a and vec b are equally inclined to coplanar vector vec c , then vec c can be a. (| vec a|)/(| vec a|+2| vec b|)a+(| vec b|)/(| vec a|+| vec b|) vec b b. (| vec b|)/(| vec a|+| vec b|)a+(| vec a|)/(| vec a|+| vec b|) vec b c. (| vec a|)/(| vec a|+2| vec b|)a+(| vec b|)/(| vec a|+2| vec b|) vec b d. (| vec b|)/(2| vec a|+| vec b|)a+(| vec a|)/(2| vec a|+| vec b|) vec b

CENGAGE ENGLISH-VECTOR ALGEBRA-All Questions
  1. Let two non-collinear unit vector hat a a n d hat b form an acute a...

    Text Solution

    |

  2. Let vec a= hat i+2 hat j+ hat k , vec b= hat i- hat j+ hat ka n d vec...

    Text Solution

    |

  3. If vec a , vec b and vec c are three non-zero, non coplanar vecto...

    Text Solution

    |

  4. The unit vector which is orthogonal to the vector 3 hat j+2 hat j+6 ...

    Text Solution

    |

  5. If vec a and vec b are unequal unit vectors such that ( vec a- vec ...

    Text Solution

    |

  6. If veca,vecb,vecc are 3 unit vectors such that vecaxx(vecbxxvecc)=vec...

    Text Solution

    |

  7. If in triangle A B C , vec A B= vec u/(| vec u|)- vec v/(| vec v|)a n ...

    Text Solution

    |

  8. A vector vec d is equally inclined to three vectors vec a= hat i+ ...

    Text Solution

    |

  9. If axx(bxxc)=(axxb)xxc , then ( vec cxx vec a)xx vec b= vec0 b. vec cx...

    Text Solution

    |

  10. If hat a , hat b ,a n d hat c are three unit vectors inclined to ea...

    Text Solution

    |

  11. Let the pairs a , b,and c ,d each determine a plane. Then the planes a...

    Text Solution

    |

  12. P(vec p) and Q(vec q) are the position vectors of two fixed points and...

    Text Solution

    |

  13. Two adjacent sides of a parallelogram A B C D are 2 hat i+4 hat j-5 ...

    Text Solution

    |

  14. If vec a and vec b are two unit vectors and theta is the angle between...

    Text Solution

    |

  15. If vec a , vec b , vec c are unit vectors such that vec adot vec b=0...

    Text Solution

    |

  16. Let vec a= hat i+ hat j ; vec b=2 hat i- hat kdot Then vector vec r ...

    Text Solution

    |

  17. If vec a and vec b are two vectors, such that vec a.vec b<0 and | ve...

    Text Solution

    |

  18. vec a , vec b , and vec c are three vectors of equal magnitude. The an...

    Text Solution

    |

  19. If vec a , vec ba n d vec c are three mutually perpendicular vect...

    Text Solution

    |

  20. Let vec aa n d vec b be two non-collinear unit vector. If vec u= vec...

    Text Solution

    |