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If vec alpha and vec beta are non-collin...

If `vec alpha` and `vec beta` are non-collinear vectors and `vec a=(x+4y) vec alpha+ (2x+y+1) vec beta` and `vec b= (y-2x+2) vec alpha + (2x-3y-1) beta`, find x and y so that `3 vec a= 2 vec b`.

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PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Using vectors, prove that the following point are collinear: (-1,2),...

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  2. Find the unknown x if the points (2,4), (7,x) and (-1,1) are collinear...

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  3. If vec alpha and vec beta are non-collinear vectors and vec a=(x+4y) v...

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  4. If the position vectors of the vertices A,B and C of triangle ABC are ...

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  5. Find the length of the vector 3 hat i+ 4 hat j- 12 hat k.

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  6. Find the components o fteh vector vec AB where A and B are the points(...

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  7. Find the coordinates of the final point of vector vec v whose componen...

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

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  9. Find the unit vector in the direction of 12 hat i- 5 hat k.

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  10. Find a unit vector parallel to the sum of the vector vec a= hat i+ hat...

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  11. Show that the points A,B and C whose position vectors are repectively ...

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  12. Find the unit vector in the direction of sum of vectors -2 hat i- 3 ha...

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  13. If vec AB= a underset 1 hat i+ a underset 2 hat j+ a underset hat k an...

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  14. Find a unit vector in the direction of vec a- 2 vec b+ 3 vec c if vec ...

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  15. Find the points of trisection of [PQ] if the position vectors of P and...

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  16. Show that the point A,B,C and D whose position vectors are respectivel...

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  17. The position vectors of the points A, B, C and D are respectively 4 ha...

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  18. Find the magnitude and components of the vector 2(-1,0,3) + 3(1,1,2)-(...

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  19. Prove that the points A (1,2,3), B(2,3,1) and C(3,1,2) are the vertice...

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  20. Prove that the points (1,1,1),(-2,4,1),(-1,5,5) and (2,2,5) taken in o...

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