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If vec aa n d vec b are position vector...

If ` vec aa n d vec b` are position vectors of points `Aa n dB` respectively, then find the position vector of points of trisection of `A B` .

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To find the position vectors of the points of trisection of the line segment joining points A and B, we will use the section formula. We denote the position vectors of points A and B as \( \vec{a} \) and \( \vec{b} \) respectively. ### Step-by-Step Solution: 1. **Understanding Trisection**: The points of trisection divide the line segment AB into three equal parts. Thus, we will have two points, C and D, such that AC = CD = DB. 2. **Using the Section Formula**: ...
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RD SHARMA-ALGEBRA OF VECTORS-Solved Examples And Exercises
  1. Show that the found points A ,B ,C ,D with position vectors vec a , v...

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  2. Let vec a , vec b , vec c be the position vectors of three distinct p...

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  3. If vec aa n d vec b are position vectors of points Aa n dB respective...

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  4. If vec aa n d vec b are position vectors of Aa n dB respectively, fin...

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  5. If vec c = 3vec a+4vec b and 2vec c =vec a -3vec b, show that (i) vec ...

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  6. Find the position vectors of the points which divide the join of th...

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  7. Let O be the centre of a regular hexagon A B C D E F . Find the sum of...

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  8. For any two vectors vec aa n d vec b , prove that | vec a+ vec b|lt=|...

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  9. IF P1, P2, P3, P4 are points in a plane or space and O is the origin o...

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  10. Using vectors, find the value of lambda such that the points (lambda,...

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  11. If vec a , vec b are any two vectors, then give the geometrical in...

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  12. If vec P O+ vec O Q= vec Q O+ vec O R , show that the point, P ,Q ,R ...

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  13. If the sum of two unit vectors is a unit vector, prove that the mag...

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  14. If vec aa n d vec b are the vectors determined by two adjacent sides ...

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  15. Vectors drawn the origin O to the points A , Ba n d C are respectively...

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  16. If vec aa n d vec b represent two adjacent sides vec A Ba n d vec B ...

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  17. Let vec a , vec b , vec c , vec d be the position vectors of the four...

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  18. Find a vector of magnitude 11 in the direction opposite to that of ve...

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  19. Find the unit vector in the direction of 3 hat i-6 hat j+2 hat k .

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  20. If vec a is a position vector whose tip is (1,-3)dot Find the coordin...

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