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Show that the four points `P ,\ Q ,\ R ,\ S` with position vectors ` vec p ,\ vec q ,\ vec r ,\ vec s` respectively such that `5 vec p-2 vec q+6 vec r-9 vec s= vec0,` are coplanar. Also find the position vector of the point of intersection of the line segments PR and QS.

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RD SHARMA ENGLISH-ALGEBRA OF VECTORS-All Questions
  1. If vec a , vec b are the position vectors of A , B respectively, find...

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  2. Show that the found points A ,B ,C ,D with position vectors vec a , v...

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  3. Show that the four points P ,\ Q ,\ R ,\ S with position vectors vec ...

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  4. The vertices A , B , C of triangle A B C have respectively position...

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  5. Evaluate inte^(5x)\dx

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  6. If O is a point in space, A B C is a triangle and D , E , F are ...

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  7. Show that the sum of three vectors determined by the medians of a t...

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  8. A B C D is parallelogram and P is the point of intersection of its dia...

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  9. Show that the line segments joining the mid-points of opposite side...

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  10. A B C D are four points in a plane and Q is the point of interse...

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  11. Evaluate int\ x^7+sin2x\dx

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  12. Find the values of x and y so that the vectors 2 hat i+3 hat jand x h...

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  13. ABCD is a parallelogram. If the coordinates of A ,\ B ,\ C\ a r e\ (2,...

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  14. Find the vector of magnitude 5 units which is parallel to the vector 2...

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  15. Find the components along the coordinates axes of the position vector ...

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  16. Find the components along the coordinates axes of the position vector ...

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  17. Find the components along the coordinates axes of the position vector ...

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  18. Find the components along the coordinates axes of the position vector ...

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  19. Find the scalar and vector components of the vector with initial point...

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  20. Write down a unit vector in XY-plane, making an angle of 30° with t...

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