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If the vector vec a= x vec i + y vec j +...

If the vector `vec a= x vec i + y vec j + 2 vec k` is perpendicular to the vector `vec b = vec i - vec j + vec k` and the scalar product of `vec a` and `vec c= vec i + 2 vec j` is equal to 4 then x= ________ and y=__________.

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A DAS GUPTA-Product of two Vectors-Exercise
  1. A , B , Ca n dD are any four points in the space, then prove that |...

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  2. If the angle between the vectors x vec i + vec j - vec k and vec i + x...

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  3. If the vector vec a= x vec i + y vec j + 2 vec k is perpendicular to t...

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  4. If vec a is a vector of magnitude 50 and parallel to vec b= 6 vec i - ...

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  5. If vec a , vec b ,a n d vec c are unit vectors such that vec a+ vec ...

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  6. Prove that , vec(a) xx ( vec (b) + vec(c)) + vec(b) xx (vec(c) + ...

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  7. If vec a and vec b are vectors, each of magnitude 3 then |vec a+ vec ...

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  8. If vecA = (1, 1, 1), vecC = (0,1,-1) are given vectors, then prove tha...

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  9. Find a unit vector perpendicular to the plane determined by the poi...

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  10. Let beta = 4hati + 3hatj and vec gamma be two vectors perpendicular to...

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  11. If |vec a|=3,|vec b|=5,|vec c|=7 and vec a+vec b+vec c=0 then angle be...

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  12. The conditions under which the vector vec P + vec Q and vec P - vec Q ...

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  13. Let vec O A- vec a , hat O B=10 vec a+2 vec ba n d vec O C= vec b ,w ...

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  14. Vector vec O A= hat i+2 hat j+2 hat k turns through a right angle ...

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  15. A vector a has components a1,a2,a3 in a right handed rectangular cart...

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  16. If vec a * vec b = vec a * vec c then

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  17. If vec(A)+vec(B)+vec(C )=0 then vec(A)xx vec(B) is

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  18. If vec a xx vec b= vec b xx vec c != vec 0 then which one is true wh...

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  19. A, B, C and D are four points in a plane with position vectors vec a,v...

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  20. If |vec a|= |vec b|= 1 and |vec a xx vec b|=1 then

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