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If AC and BD are the diagonals of a quad...

If AC and BD are the diagonals of a quadrilateral ABCD, prove that its area is equal to `1/2 |vec (AC) xx vec (BD)|`.

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A DAS GUPTA-Product of two Vectors-Exercise
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  2. Given the vectors vec A , vec B ,a n d vec C form a triangle such tha...

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  3. If AC and BD are the diagonals of a quadrilateral ABCD, prove that its...

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  4. A , B , Ca n dD are any four points in the space, then prove that |...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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