Home
Class 12
MATHS
If the position vectors of two given poi...

If the position vectors of two given points A and B be `8hat(i)+3hat(j)+2hat(k) " and " 2hat(i)-5hat(j)+3hat(k)` respectively, find the magnitude and direction of `vec(AB)`.

Text Solution

Verified by Experts

The correct Answer is:
Required magnitude of `vec(AB) " is " sqrt(101)` its direction makes an angle `cos^(-1)(6/sqrt(101))` with `vec(OX)`.
Promotional Banner

Topper's Solved these Questions

  • VECTOR

    CHHAYA PUBLICATION|Exercise EXERCISE - MCQ|12 Videos

  • VECTOR

    CHHAYA PUBLICATION|Exercise EXERCISE - VERY SHORT ANSWER TYPE QUESTIONS|17 Videos

  • VECTOR

    CHHAYA PUBLICATION|Exercise SAMPLE QUESTIONS FOR COMPETITIVE EXAMINATION|18 Videos

  • TRIGONOMETRIC RATIOS [OR FUNCTIONS] OF POSITIVE ACUTE ANGLES

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Exams (Assertion -Reason Type )|2 Videos

Similar Questions

Explore conceptually related problems

The position vectors of two given points P and Q are 8hat(i)+3hat(j) " and " 2hat(i)-5hat(j) respectively, find the magnitude and direction of the vector vec(PQ)

The position vectors of the points A and B are 3hat(i)-hat(j)+7hat(k) " and " 4hat(i)-3hat(j)-hat(k) , find the magnitude and direction cosines of vec(AB)

If the position vectors of the points P and Q are 2hat(i)+hat(k) " and " -3hat(i)-4hat(j)-5hat(k) respectively, then vector vec(OP) is -

(i) If the position vectors of the points A, B, C be 5hat(i)+3hat(j)+4hat(k), hat(i)+5hat(j)+hat(k) " and " -3hat(i)+7hat(j)-2hat(k) respectively, then show that the points B bisects the line-segment bar(AC) . (ii) The position vectors of the points P and Q are 5hat(i)-12hat(j)+5hat(k) " and " -4hat(i)+3hat(j)-hat(k) respectively. Find the position vectors of the trisection points of the line-segment bar(PQ) .

If the position vectors of the points A, B, C are -2hat(i)+2hat(j)+2hat(k), 2hat(i)+3hat(j)+3hat(k) " and " -hat(i)-2hat(j)+3hat(k) respectively, show that ABC is an isosceles triangle.

If the position vectors of the points A, B C are 3hat(i)-4hat(j)-4hat(k), 2hat(i)-hat(j)+hat(k) " and " hat(i)-3hat(j)-5hat(k) respectively. Show that ABC is right-angled triangle.

The position vectors of the points A,B, and C are 2hat(i)+4hat(j)-hat(k), 4hat(i)+5hat(j)+hat(k) " and " 3hat(i)+6hat(j)-3hat(k) respectively. Show that the points form a right-angled triangle.

The position vectors of the points A, B and C are 2hat(i)+6hat(j)-hat(k), hat(i)+2hat(j)+4hat(k) " and " 3hat(i)+10hat(j)-6hat(k) respectively. Show that the points A, B and C are collinear.

The position vectors of the points A, B, C and D are hat(i)+hat(j)+hat(k), 2hat(i)+3hat(j), 3hat(i)+5hat(j)-2hat(k) " and " -hat(j)+hat(k) respectively. Show that vec(AB) " and " vec(CD) are parallel and find the ratio of their moduli.

Points A and B have position vector vec(a)=-3hat(i)+2hat(j)+7hat(k) and vec(b)=3hat(i)+4hat(j)-5hat(k) respectively. Find : The direction ratios of vec(AB)

CHHAYA PUBLICATION-VECTOR-ILLUSTRATIVE EXAMPLES
  1. If vec(a)=2hat(i)+5hat(j)-2hat(k) " and " vec(b)=hat(i)-hat(j)+hat(k),...

    Text Solution

    |

  2. If the position vectors of two given points A and B be 8hat(i)+3hat(j)...

    Text Solution

    |

  3. The position vectors of the points A, B and C are 2hat(i)+6hat(j)-hat(...

    Text Solution

    |

  4. Determine the values of p and q for which the vectors phat(i)+2hat(j)+...

    Text Solution

    |

  5. The position vectors of the points A, B, C and D are hat(i)+hat(j)+hat...

    Text Solution

    |

  6. show by vector method that the points (2, -1, 3), (3, -5, 1) and (-1, ...

    Text Solution

    |

  7. Using vector method show that the points (7, 9), (3, -7) and (-3, 3) f...

    Text Solution

    |

  8. The position vectors of the points A,B, and C are 2hat(i)+4hat(j)-hat(...

    Text Solution

    |

  9. Write the direction ratios of the vector 2hat(i)-hat(j)-2hat(k) and he...

    Text Solution

    |

  10. Find a vector of magnitude 14 in the direciton of the vector -3hat(i)+...

    Text Solution

    |

  11. If vec(a) " and "vec(b) are non-collinear vectors and vec(p)=(x+4y)vec...

    Text Solution

    |

  12. Prove that the points with position vectors 60hat(i)+3hat(j), 40hat(i)...

    Text Solution

    |

  13. For the vectors vec(a) " and " vec(b) show that (i) abs(vec(a)+vec(b...

    Text Solution

    |

  14. (i) If the position vectors of the points A, B, C be 5hat(i)+3hat(j)+...

    Text Solution

    |

  15. If the magnitude of difference of two unit vectors in sqrt(3), then sh...

    Text Solution

    |

  16. ABCDEF is a regular hexagon. If vec(AB)=vec(a) " and " vec(BC)=vec(b),...

    Text Solution

    |

  17. Using vector method show that the diagonals of a parallelogram bisect ...

    Text Solution

    |

  18. By vector method prove that the three medians of a triangle are concur...

    Text Solution

    |

  19. Using vector method show that the line joining the middle points of tw...

    Text Solution

    |

  20. If G be the centroid of the triangle ABC, then prove that vec(GA)+vec(...

    Text Solution

    |