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If vec(A) +vec(B) = vec(C) and A^(2) +B^...

If `vec(A) +vec(B) = vec(C)` and `A^(2) +B^(2) = C^(2)`, then prove that `vec(A)` and `vec(B)` are perpendicular to each other.

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SL ARORA-Motion in a Plane-Example
  1. Determine the angles which the vector vec(A) = 5 hati + 0 hatj +5hat...

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  2. If unit vectors hat(a) and hat(b) are inclined at angle theta, then pr...

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  3. If vec(A) +vec(B) = vec(C) and A^(2) +B^(2) = C^(2), then prove that v...

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  4. Motion in two dimensions, in a plane can be studied by expressing posi...

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  5. Prove that the vectors vec(A) = 2hati - 3hatj - hatk and vec(B) =- 6 h...

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  6. Calculate the area of a paralleleogram whose two adjacent sides are fo...

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  7. If vec(A) and vec(B) denpte the sides of a parallelogram and its area ...

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  8. The unit vector perpendicular to vec A = 2 hat i + 3 hat j + hat k and...

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  9. Find a unit vector perpendicular to each one of the vectors vec(a) = 4...

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  10. Determine the sine of the angle between the vectors ( 3 hat i+ 3hat j+...

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  11. Show that (vec(A) - vec(B)) xx (vec(A) +vec(B)) = 2(vec(A) xx vec(B))

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  12. For any three vectors vec(A), vec(B) and vec(C) prove that vec(A) x...

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  13. For any to vectors vec A and vec B, prove that | vec A xx vec B|^2 ...

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  14. Find vec(A).vec(B) if |vec(A)| = 2, |vec(B)| = 5 and |vec(A) xx vec(B)...

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  15. Find the area of the rriangle formed by the tips of the vectors, ve...

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  16. Find the magnitude and direction cosines of the torque about the point...

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  17. Find the area of parallelogram whose diagonals are the vectors 3 hat i...

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  18. In any triangle ABC, prove that a sin A-b sin B -=c sin (A-B).

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  19. If vec a ,\ vec b ,\ vec c are three vectors such that vec adot...

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  20. If vec A=hat i + 2 hat j -3 hat k, vec B =2 hat I -hat j + hat k and...

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