Home
Class 12
MATHS
Three vectors vec(A) = 2hat(i) - hat(j) ...

Three vectors `vec(A) = 2hat(i) - hat(j) + hat(k), vec(B) = hat(i) - 3hat(j) - 5hat(k)`, and `vec(C ) = 3hat(i) - 4hat(j) - 4hat(k)` are sides of an :

Text Solution

Verified by Experts

The correct Answer is:
`cos^(-1)sqrt((6)/(41))`
Promotional Banner

Topper's Solved these Questions

  • VECTOR ALGEBRA

    MODERN PUBLICATION|Exercise Questions From NCERT Exemplar (Example)|3 Videos

  • VECTOR ALGEBRA

    MODERN PUBLICATION|Exercise EXERCISE 10 (a) Short Answer Type Questions|21 Videos

  • VECTOR ALGEBRA

    MODERN PUBLICATION|Exercise CHAPTER TEST 10|12 Videos

  • THREE DIMENSIONAL GEOMETRY

    MODERN PUBLICATION|Exercise CHAPTER TEST 11|11 Videos

Similar Questions

Explore conceptually related problems

The three vector vec(A) = 3hat(i)-2hat(j)+hat(k), vec(B)= hat(i)-3hat(j)+5hat(k) and vec(C )= 2hat(i)+hat(j)-4hat(k) from

Given the three vectors vec(a) = - 2hati + hat(j) + hat(k), vec(b) = hat(i) + 5hat(j) and vec(c) = 4hat(i) + 4hat(j) - 2hat(k) . The projection of the vector 3vec(a) - 2vec(b) on the vector vec(c) is

If vec(a) = hat(i) - hat(j) + hat(k). vec(b) = 2hat(i) + 3hat(j) + 2hat(k) and vec(c ) = hat(i) + m hat(j) + n hat(k) are three coplanar vectors and |vec(c )| = sqrt6 , then which one of the following is correct?

Vector vec(A)=hat(i)+hat(j)-2hat(k) and vec(B)=3hat(i)+3hat(j)-6hat(k) are :

a. Prove that the vector vec(A)=3hat(i)-2hat(j)+hat(k) , vec(B)=hat(i)-3hat(j)+5hat(k), and vec(C )=2hat(i)+hat(j)-4hat(k) from a right -angled triangle. b. Determine the unit vector parallel to the cross product of vector vec(A)=3hat(i)-5hat(j)+10hat(k) & =vec(B)=6hat(i)+5hat(j)+2hat(k).

Show that the vectors : vec(a)=hat(i)-2hat(j)+3hat(k), vec(b)=-2hat(i)+3hat(j)-4hat(k) and vec(c )=hat(i)-3hat(j)+5hat(k) are coplanar.

Find the volume of the parallelepiped whose edges are represented by the vectors vec(a)=(2hat(i)-3hat(j)+4hat(k)), vec(b)=(hat(i)+2hat(j)-hat(k)) and vec(c)=(3hat(i)-hat(j)+2hat(k)) .

For what value of 'lambda' are the following vectors coplanar ? vec(a)=2hat(i)-4hat(j)+5hat(k), vec(b)=hat(i)-lambda hat(j)+hat(k) and vec(c )= 3hat(i)+2hat(j)-5hat(k) .

Find the area of the parallelogram whose adjacent sides are represented by the vectors (i) vec(a)=hat(i) + 2 hat(j)+ 3 hat(k) and vec(b)=-3 hat(i)- 2 hat(j) + hat(k) (ii) vec(a)=(3 hat(i)+hat(j) + 4 hat(k)) and vec(b)= ( hat(i)- hat(j) + hat(k)) (iii) vec(a) = 2 hat(i)+ hat(j) +3 hat(k) and vec(b)= hat(i)-hat(j) (iv) vec(b)= 2 hat(i) and vec(b) = 3 hat(j).

verify that vec(a) xx (vec(b)+ vec(c))=(vec(a) xx vec(b))+(vec(a) xx vec(c)) , "when" (i) vec(a)= hat(i)- hat(j)-3 hat(k), vec(b)= 4 hat(i)-3 hat(j) + hat(k) and vec(c)= 2 hat(i) - hat(j) + 2 hat(k) (ii) vec(a)= 4 hat(i)-hat(j)+hat(k), vec(b)= hat(i)+hat(j)+ hat(k) and vec(c)= hat(i)- hat(j)+hat(k).

MODERN PUBLICATION-VECTOR ALGEBRA -Frequently Asked Questions (Example)
  1. If ā,b,c are three vectors such that |veca |= 5, |vecb| = 12 and | ...

    Text Solution

    |

  2. If vec(a) , vec(b) and vec(c ) be three vectors such that vec(a) + vec...

    Text Solution

    |

  3. Three vectors vec(A) = 2hat(i) - hat(j) + hat(k), vec(B) = hat(i) - 3h...

    Text Solution

    |

  4. If vec a ,\ vec b ,\ vec c are three mutually perpendicular vectors...

    Text Solution

    |

  5. Find a vector vec a of magnitude 5sqrt(2) making an angle pi/4 with x-...

    Text Solution

    |

  6. Let vec(A)=4hat(i)+5hat(j)-hat(k), vec(b)=hat(i)-4hat(j)+5hat(k) and v...

    Text Solution

    |

  7. If with reference to a right handed system of mutually perpendicula...

    Text Solution

    |

  8. If vectors vec a\ a n d\ vec b\ are such that | vec a|=3,\ | vec b|...

    Text Solution

    |

  9. If 'theta' is the angle between the vectors : vec(a)=hat(i)+2hat(j)+3h...

    Text Solution

    |

  10. Find 'lambda' and 'mu' if : (hat(i)+3hat(j)+9hat(k))xx(3hat(i)-lam...

    Text Solution

    |

  11. If vec a= hat i+ hat j+ hat kand vec b= hat j- hat k ,find a vect...

    Text Solution

    |

  12. If vec(r )=x hat(i)+y hat(j)+x hat(k), find : (vec(r )xx hat(i)).(vec...

    Text Solution

    |

  13. If vec(a) xx vec(b)= vec(c) xx vec(d) and vec(a) xx vec(c) =vec(b) xx ...

    Text Solution

    |

  14. Find a vector of magnitude 7 units, which is perpendicular to two vect...

    Text Solution

    |

  15. Find the area of the parallelogram whose adjacent sides are determined...

    Text Solution

    |

  16. Find the area of a parallelogram whose adjacent sides are given by th...

    Text Solution

    |

  17. Find the area of a triangle having the pointsA(1, 1, 1), B(1, 2, 3)and...

    Text Solution

    |

  18. If vec(a)=2hat(i)-3hat(j)+4hat(k) and vec(b)=5hat(i)+hat(j)-hat(k) r...

    Text Solution

    |

  19. If vec(a), vec(b), vec(c ) are the position vectors of the vecrtices A...

    Text Solution

    |

  20. Largange's Identify. Prove that (vec(a)xx vec(b))^(2)=|vec(a)|^(2)|vec...

    Text Solution

    |