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If a\ a n d\ b ar non collinear vector s...

If `a\ a n d\ b` ar non collinear vector such that `x_1 vec a+y_1 vec b=x_2 vec a+y_2 vec b` , then prove that `x_1=x_2a n d\ y_1=y_2dot`

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RD SHARMA ENGLISH-ALGEBRA OF VECTORS-All Questions
  1. If vec a and vec b are non-collinear vectors and vectors vecalpha=(x...

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  2. A B C D is a parallelogram. E ,F are mid-points of B C ,C D respective...

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  3. If a\ a n d\ b ar non collinear vector such that x1 vec a+y1 vec b=x2 ...

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  4. Show that the vectors a, b, c given by vec a= hat i+2 hat j+3 hat k ,...

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  5. A vector vec O P is inclined to O X at 50^0 and O Y at 60^0 . Find th...

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  6. If a vector makes angles alpha,beta,gamma. with . OX ,O Ya n dO Z ...

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  7. A B C D is a parallelogram. If L and M are the mid-points of B C and D...

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  8. Find a unit vector in the direction of the resultant of the vectors...

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  9. Find the position vector of the mid-point of the vector joining the...

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  10. Show that the line joining one vertex of a parallelogram to the mid...

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  11. Let vec a , vec b, vec c be three non-zero vectors such that any two ...

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  12. If vec a , vec b are the position vectors of the points (1,-1),(-2,m...

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  13. Find the position vector of a point A in space such that vec O A is i...

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  14. Show that the points A(6,-7,0),B(16 ,-19 ,-4),C(0,3,-6)a n d D(2,-5,1...

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  15. Prove that the lines joining the vertices of a tetrahedron to the ce...

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  16. Find a vector vec r of magnitude 3sqrt(2)u n i t s which makes an an...

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  17. Let vec a= hat i+2 hat ja n d vec b=2 hat i+ hat jdoti s |vec a|=| ve...

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  18. Three vectors of magnitude a ,2a ,3a meet in a point and their directi...

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  19. Show that the vectors vec a-2 vec b+3 vec c , vec a-3 vec b+5 vec ca ...

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  20. Find the angles at which the vector 2 hat i- hat j+2 hat k is inclined...

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