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Prove that the vectors vec(A) = 2hati - ...

Prove that the vectors `vec(A) = 2hati - 3hatj - hatk` and `vec(B) =- 6 hati + 9hatj +3hatk` are parallel.

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Prove that the vectors vec(A) = 4 hati +3hatj +hatk and vec(B) = 12 hati + 9 hatj +3 hatk are parallel to each other.

Determine the area of the parallelogram whose adjacent sides are formed by the vectors vec(A) = hati - 3hatj + hatk and vec(B) = hati + hatj + hatk .

Find the unit vector parallel to the resultant of the unit vectors vec(A) = 2 hati - 6 hatj - 3hatk and vec(B) = 4 hati +3hatj - hatk .

Prove that the vectors vec(A) = hati +2 hatj +3hatk and vec(B) = 2hati - hatj are perpendicular to each other.

Find a vector whose length is 7 and which is perpendicular to each of the vectors, vec(A) = 2 hati - 3hatj + 6hatk and vec(B) = hati +hatj - hatk

Find the angle between the vectors vec(A) = 2 hati - 4hatj +6 hatk and vec(B) = 3 hati + hatj +2hatk .

Find a unit vector perpendicular the vectors vec(A) = 4 hati = hatj +3 hatk and vec(B) =- 2hati + hatj - 2hatk .

Find the sine of the angle between the vectors vec(A) = 3 hati - 4hatj +5hatk and vec(B) = hati - hatj +hatk .

Find the angle between the vertors vec(A) = hati + 2hatj - hatk and vec(B) = - hati +hatj - 2hatk .

Find unit vector parallel to the resultant of the vectors vec(A) = hati +4hatj +2hatk and vec(B) = 3hati - 5hatj +hatk .

SL ARORA-Motion in a Plane-Example
  1. If vec(A) +vec(B) = vec(C) and A^(2) +B^(2) = C^(2), then prove that v...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  18. 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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  19. A cyclist moves along a circular path of radius 70 m. If he completes ...

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  20. A cyclist moves along a circular path of radius 70 m. If he completes ...

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