Home
Class 12
MATHS
If vec(a)=4vec(i)-3hat(j) " and " vec(b)...

If `vec(a)=4vec(i)-3hat(j) " and " vec(b)=-2hat(i)+5hat(j)` are the position vectors of the points A and B respectively, find
(i) the position vector of the middle point of the line-segment `bar(AB)`,
(ii) the position vectors of the points of trisection of the line-segment `bar(AB)`.

Text Solution

Verified by Experts

The correct Answer is:
`"(i) " hat(i)+hat(j) " (ii) " 2hat(i)-1/3hat(j) " and " 7/3hat(j)`
Promotional Banner

Topper's Solved these Questions

  • VECTOR

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

  • VECTOR

    CHHAYA PUBLICATION|Exercise EXERCISE - LONG ANSWER TYPE QUESTIONS|21 Videos

  • VECTOR

    CHHAYA PUBLICATION|Exercise EXERCISE - MCQ|12 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 vecors of the points A and B are 4hat(i)-3hat(j)+5hat(k) " and " -2hat(i)+3hat(j)+2hat(k) respectively, find (i) the position vector of the middle point of the line-segment bar(AB) , (ii) the position vector of the points of trisection of the line-segment bar(AB) .

Let vec(a) " and " vec(b) be the position vectors of two given points P and Q respectively. To find the position vector of the point R which divides the line segment bar(PQ) internally in the ratio m:n.

The position vectors of the points A and B are 2vec(a)+vec(b) " and " vec(a)-3vec(b) . If the point C divides the line-segment bar(AB) externally in the ratio 1:2, then find the position vector of the point C. Show also that A is the midpoint of the line-segment bar(CB) .

If vec(OA)=hat(i)-2hat(k) " and " vec(OB)=3hat(i)-2hat(j) then the direction cosines of the vector vec(AB) are -

If vec(a)=2hat(i)+3hat(j)-4hat(k) " and " vec(b)=hat(i)+2hat(j)+hat(k) , then find (vec(a)+vec(b)) " and " abs(vec(a)+vec(b)).

If vec(a)=2hat(i)-5hat(j)+3hat(k) " and " vec(b)=hat(i)-2hat(j)-4hat(k) , find the value of abs(3vec(a)+2vec(b)).

(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 vec(a)=hat(i)+2hat(j)-hat(k) " and " vec(b)=3hat(i)+hat(j)-5hat(k) , find a unit vector in a direction parallel to vector (vec(a)-vec(b)) .

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 -

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)

CHHAYA PUBLICATION-VECTOR-EXERCISE - VERY SHORT ANSWER TYPE QUESTIONS
  1. Define a vector from the geometrical concept.

    Text Solution

    |

  2. Write two different vectors having the same magnitude.

    Text Solution

    |

  3. Write two different vectors having the same direction.

    Text Solution

    |

  4. Define the position vector of a point with respect to an origin. If ve...

    Text Solution

    |

  5. Define a vector and a unit vector. Find in terms of vector vec(a) a un...

    Text Solution

    |

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

    Text Solution

    |

  7. If vec(a)=2hat(i)+3hat(j)-4hat(k) " and " vec(b)=hat(i)+2hat(j)+hat(k)...

    Text Solution

    |

  8. If vec(alpha)=2hat(i)-5hat(j)+4hat(k) " and " vec(beta)=hat(i)-4hat(j)...

    Text Solution

    |

  9. Show that the vectors -hat(i)+hat(j), -4hat(i)-6hat(j) " and " 5hat(i)...

    Text Solution

    |

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

    Text Solution

    |

  11. Using vector method show that the points A(-5,7), B(-4,5) and C(1, -5)...

    Text Solution

    |

  12. If vec(a)=hat(i)+hat(j) " and " vec(b)=4hat(i)-hat(j), find a unit vec...

    Text Solution

    |

  13. The position vectors of two given points P and Q are 8hat(i)+3hat(j) "...

    Text Solution

    |

  14. If vec(a)=4vec(i)-3hat(j) " and " vec(b)=-2hat(i)+5hat(j) are the posi...

    Text Solution

    |

  15. Find the vector from the origin to the intersection of the medians of ...

    Text Solution

    |

  16. (i) Determine the value of p for which the vectors phat(i)-5hat(j) " a...

    Text Solution

    |

  17. The position vectors of the points A and B are 3hat(i)-hat(j)+7hat(k) ...

    Text Solution

    |