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Show that the points with position vectors ` vec a-2 vec b+3 vec c ,-2 vec a+3 vec b+2 vec ca n d-8 vec a+13 vec b` are collinear whatever be ` vec a , vec b , vec cdot`

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Show that the point A ,B ,C with position vectors vec a-2 vec b+3 vec c ,2 vec a+3 vec b-4 vec c and -7 vec b+10 vec c are collinear.

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Show that the vectors 2 vec a- vec b+3 vec c , vec a+ vec b-2 vec ca n d vec a+ vec b-3 vec c are non-coplanar vectors (where vec a , vec b , vec c are non-coplanar vectors)

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If vec a , vec b are two non-collinear vectors, prove that the points with position vectors vec a+ vec b , vec a- vec b and vec a+lambda vec b are collinear for all real values of lambdadot

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Let vec a , vec ba n d vec c , be non-zero non-coplanar vectors. Prove that: vec a-2 vec b+3 vec c ,-2 vec a+3 vec b-4 vec ca n d vec c-3 vec b+5 vec c are coplanar vectors. 2 vec a- vec b+3 vec c , vec a+ vec b-2 vec ca n d vec a+ vec b-3 vec c are non-coplanar vectors.

RD SHARMA ENGLISH-ALGEBRA OF VECTORS-All Questions
  1. If the position vector vec a of a point (12 ,n) is such that | vec a|...

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  2. If A=(0,1)B=(1,0),C=(1,2),D=(2,1) , prove that vec A B= vec C Ddot

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  3. Show that the points with position vectors vec a-2 vec b+3 vec c ,-2 ...

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  4. Find the position vector of a point R which divides the line joining ...

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  5. If D is the mid-point of the side B C of a triangle A B C , prove that...

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

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

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  8. If vec a and vec b are position vectors of points Aa n dB respectivel...

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

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

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

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

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

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

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

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  16. If vec a , vec b are any two vectors, then give the geometrical int...

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

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

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

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

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