Home
Class 12
MATHS
Let vec a(x)=(sin x) hat i+(cosx) hat j...

Let ` vec a(x)=(sin x) hat i+(cosx) hat j a n d vec b(x)=(cos2x) hat i+(sin2x) hat j` be two variable vectors `(x in R)dot` Then ` vec a(x)a n d vec b(x)` are a. collinear for unique value of `x` b. perpendicular for infinite values of `x` c. zero vectors for unique value of `x` d. none of these

Promotional Banner

Topper's Solved these Questions

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

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|6 Videos

  • VECTORS TRIPLE PRODUCTS, RECIPROCAL SYSTEM OF VECTORS

    CENGAGE PUBLICATION|Exercise DPP 2.4|20 Videos

Similar Questions

Explore conceptually related problems

Find vec adot vec b when: vec a= hat j- hat k\ a n d\ vec b=2 hat i+3 hat j-2 hat k

If vec a=x hat i+(x-1) hat j+ hat k and vec b=(x+1) hat i+ hat j+a hat k make an acute angle AAx in R , then find the values of adot

For given vector, vec a = 2 hat i j +2 hat k and vec b = - hat i + hat j - hat k , find the unit vector in the direction of the vector vec a + vec b .

Find vec axx vec b ,\ if\ vec a=2 hat i+ hat k\ a n d\ vec b= hat i+ hat j+ hat kdot

Let vec a= hat i+2 hat j+ hat k , vec b= hat i- hat j+ hat ka n d vec c= hat i+ hat j- hat kdot Then find [vec a vec b vec c]

If vec (a) = 2 hat (i) - hat (j ) and vec (b) = 3 hat (i) - 2 hat (j) + 4 hat (k) , then the value of vec (a) xx vec (b) is -

If vec a=x hat i+y hat j+z hat k , vec b=y hat i+z hat j+x hat k and vec c=z hat i+x hat j+y hat k , then vec axx( vec bxx vec c) is

Let vec a=x hat i+12 hat j- hat k , vec b=2 hat i+2x hat j+ hat ka n d vec c= hat i+ hat kdot If the ordered set [ vec b vec c vec a] is left handed, then find the values of xdot

Let vec (a) = 2 hat (i) - 2 hat (j) + hat (k) , vec (b) = hat (j) - hat (k) and vec(c ) = - hat (i) + 3 hat (j) + 2 hat (k) be three given vectors .Find vec(a) xx vec(b)

Let vec (a) = 2 hat (i) - 2 hat (j) + hat (k) , vec (b) = hat (j) - hat (k) and vec(c ) = - hat (i) + 3 hat (j) + 2 hat (k) be three given vectors .Find angle between vec(a) and vec(b)

CENGAGE PUBLICATION-VECTOR ALGEBRA-All Questions
  1. vec a , vec ba n d vec c are three non-coplanar ,non-zero vectors an...

    Text Solution

    |

  2. The position vectors of point A ,B ,a n dC are hat i+ hat j+ hat k...

    Text Solution

    |

  3. Let vec a(x)=(sin x) hat i+(cosx) hat j a n d vec b(x)=(cos2x) hat i+...

    Text Solution

    |

  4. If vec a=2 hat i+ hat j+ hat k , vec b= hat i+2 hat j+2 hat k , vec c=...

    Text Solution

    |

  5. If vec a , vec ba n d vec c are unit vectors satisfying | vec a- v...

    Text Solution

    |

  6. If vec d= vec axx vec b+ vec bxx vec c+ vec cxx vec a is non-zero vec...

    Text Solution

    |

  7. The vector(s) which is/are coplanar with vectors hat i+ hat j+2 hat...

    Text Solution

    |

  8. Let vec a=- hat i- hat k , vec b=- hat i+ hat ja n d vec c= hat i+2 h...

    Text Solution

    |

  9. Let vec a , vec b ,a n d vec c be vectors forming right-hand traid. L...

    Text Solution

    |

  10. If the vectors vec a , vec b ,a n d vec c form the sidesB C ,C Aa n d...

    Text Solution

    |

  11. Find vec axx vec b ,\ if\ vec a=2 hat i+ hat k\ a n d\ vec b= hat i...

    Text Solution

    |

  12. Find the work done by the force F=3 hat i- hat j-2 hat k acrting on ...

    Text Solution

    |

  13. Prove that [[ vec a+ vec b, vec b+ vec c, vec c+ vec a]]=2[ [vec a, ve...

    Text Solution

    |

  14. find the angle between the vectors vec a= hat i+ hat j - hat k and ve...

    Text Solution

    |

  15. O A B C is regular tetrahedron in which D is the circumcentre of O...

    Text Solution

    |

  16. In the quadrilateral ABCD, the diagonals AC and BD are equal and perpe...

    Text Solution

    |

  17. If vece(1),vece(2),vece(3)and vecE(1),vecE(2),vecE(3) are two sets of ...

    Text Solution

    |

  18. Find the angle between the vectors vec a= hat i+hat j-hat k and vec b=...

    Text Solution

    |

  19. Given the vectors vec A , vec B ,a n d vec C form a triangle such tha...

    Text Solution

    |

  20. If vec a , vec ba n d vec c are three mutually perpendicular vecto...

    Text Solution

    |