Home
Class 11
MATHS
Which of the following statements are tr...

Which of the following statements are true.
Statement-I: `(vec(r ).vec(i)) (vec(r )xx vec(i)) + (vec(r ).vec(j)) (vec(r ) xx vec(j)) + (vec(r ).vec(k)) (vec(r )xx vec(k)) = vec(r )`
Statement-II: If `vec(a) xx vec(b)= vec(0), vec(a).vec(b)=0`, then one of `vec(a),vec(b)` is a null vector.

A

only I

B

Only II

C

neither I nor II

D

both I and II

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • VECTOR (CROSS) PRODUCT OF TWO VECTORS

    AAKASH SERIES|Exercise Exercise-II|47 Videos
  • TRIGONOMETRIC RATIOS

    AAKASH SERIES|Exercise ADDITIONAL PRACTICE EXERCISE (LEVEL - II) (PRACTICE SHEET (ADVANCED) SIGNLE ANSWER TYPE QUESTIONS)|23 Videos

Similar Questions

Explore conceptually related problems

(vec(a) xx vec(b), vec(b) xx vec(a)) =

If vec(r )= x vec(i) + y vec(j) + z vec(k) then (vec(r ) xx vec(i)).(vec(r ) xx vec(j)) + xy=

(vec(a) + vec(b)) xx (vec(a)-vec(b)) + (vec(b) + vec(c )) xx (vec(b)-vec(c )) + (vec(c )+ vec(a)) xx (vec(c ) -vec(a)) =

If vec(r )= x vec(i) + y vec(j) + z vec(k) then find (vec(r ) xx vec(i))^(2)- (vec(r )xx vec(k))^(2)

If vec(a)= vec(i) + vec(j)+ vec(k), vec(c )= vec(j)- vec(k) , then find vector vec(b) such that vec(a) xx vec(b)= vec(c ) and vec(a).vec(b)= 3

Let vec(a) + m vec(b) + n vec(c )= vec(0).vec(a) xx vec(b) + vec(b) xx vec(c ) + vec(c ) xx vec(a)= vec(0) for

If vec(a) + 2vec(b) + 4 vec(c )= vec(0) , then vec(a) xx vec(b) + vec(b) xx vec(c )+ vec(c )xx vec(a)=

If |vec(a) xx vec(b)|=6, |vec(a)|=6, (vec(a), vec(b))= (pi)/(3) , then |vec(b)| =

vec(a)= 2vec(i) + vec(j) -vec(k), vec(b)= -vec(i) + 2vec(j)- 4vec(k) and vec(c )= vec(i) + vec(j) + vec(k) , then find (vec(a) xx vec(b)).(vec(b) xx vec(c )) .

If vec(a)= 2vec(i) -vec(j) + 3vec(k), vec(b)= p vec(i) + vec(j) + q vec(k) and vec(b) xx vec(a) = vec(0) , then

AAKASH SERIES-VECTOR (CROSS) PRODUCT OF TWO VECTORS-Practice Exercise
  1. Let vec(a) + m vec(b) + n vec(c )= vec(0).vec(a) xx vec(b) + vec(b) xx...

    Text Solution

    |

  2. If |vec(a)| = |vec(b)|=2, then (vec(a) xx vec(b))^(2) + (vec(a).vec(b)...

    Text Solution

    |

  3. Which of the following statements are true. Statement-I: (vec(r ).ve...

    Text Solution

    |

  4. If r. a = r.b = r.c = 0 where a,b,c are noncoplannar, then

    Text Solution

    |

  5. A vector vec( c) perpendicular to the vectors 2vec(i) + 3vec(j)-vec(k)...

    Text Solution

    |

  6. The vectors vec(a) and vec(b) are not perpendicular and vec(c ) and ve...

    Text Solution

    |

  7. If three vectors vec(a), vec(b), vec(c ) are such that vec(a) ne vec(0...

    Text Solution

    |

  8. Assertion (A): The area of the triangle with vertices (1,2,3), (2, 5, ...

    Text Solution

    |

  9. The area of the parallelogram is 4sqrt29 sq.u. If one of adjacent side...

    Text Solution

    |

  10. ABCD is a quadrilateral with vec(AB)= vec(a), vec(AD)= vec(b) and vec(...

    Text Solution

    |

  11. The perpendicular distance from A(1, 4, -2) to BC, where B= (2, 1, -2)...

    Text Solution

    |

  12. If vec(AB)= vec(b) and vec(AC)= vec( c), then the length of the perpen...

    Text Solution

    |

  13. The torque about the point 2i + j - K of a force represented by 4i + k...

    Text Solution

    |

  14. Assertion (A): The torque about the point 3vec(i)-vec(j) + 3vec(k) of ...

    Text Solution

    |

  15. If vec(a) xx vec(b)= vec(c ) xx vec(d), vec(a) xx vec(c )= vec(b) xx v...

    Text Solution

    |

  16. (2 vec(i) + 4vec(j) + 2vec(k)) xx (2vec(i) -p vec(j) + 5vec(k))=16 vec...

    Text Solution

    |

  17. If vec(a)= vec(i) + vec(j) + vec(k), vec(b)= 2vec(i)-3vec(j) + vec(k),...

    Text Solution

    |

  18. If |bar(P)| = 2, |bar(q)| = 3 and (bar(p),bar(q)) = (pi)/6, then find ...

    Text Solution

    |

  19. If vec(u)= vec(a)- vec(b), vec(v)= vec(a) + vec(b) and |vec(a)| =|vec(...

    Text Solution

    |

  20. The vector area of the rectangle whose adjacent sides are p vec(i), q ...

    Text Solution

    |