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Show that the vector vec(A) = hati +hatj...

Show that the vector `vec(A) = hati +hatj +hatk` is perpendicular to the vector `vec(B) = - hati - hatj +2hatk`.

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A vector of magnitude sqrt2 coplanar with the vectors veca=hati+hatj+2hatk and vecb = hati + hatj + hatk, and perpendicular to the vector vecc = hati + hatj +hatk is

The componant of vector 2 hati -3 hatj +2hatk perpendicular to the vector hati + -3 hatj + hatk is-

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

The direction-cosines of te vector vec(a) = hati - hatj - 2 hatk are ,

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

The vector equation of a line passing through the point hati + 2hatj + 3hatk and perpendicular to the vectors hati +hatj + hatk and 2hati - hatj + hatk is

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SL ARORA-VECTORS-Problems For Self Practice
  1. An aeroplane taked off at an angle of 30^(@) to the horizontal. If the...

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  2. A child pulls a rope attached to a stone with a force of 80N. The rope...

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  3. Show that the vector vec(A) = hati +hatj +hatk is perpendicular to the...

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  4. Find the value of m so that the vector 3 hati - 2hatj +hatk is perpend...

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  5. For what value of a are the vectors vec(A) = a hati - 2hatj +hatk and ...

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  6. Find the angles between the following pairs of vectors: (i) vec(A) =...

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  7. Calculate the values of (i) hatj. (2hati - 3hatj +hatk) and (ii) (2hat...

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  8. A force vec(F) = 4 hati + hatj + 3hatk newton acts on a particle and d...

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  9. Under a force of 10 hati - 3 hatj +6 hatk newton, a body of mass 5 kg ...

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  10. The sum and difference of two vectors vec(A) and vec(B) are vec(A) +ve...

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  11. A force vec(F) = 5hati + 4hatj newton displaces a body through vec(S) ...

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  12. If the resultant of the vectors 3 hati +4 hatj +5 hatk and 5 hati +3 h...

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  13. Show that the vectors a =3hati - 2hatj+hatk, b=hati - 3hatj+5hatk and ...

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  14. If vectors vec(A),vec(B) and vec(C) have magnitudes 8,15 and 17 units ...

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  15. If vec A =vec B- vec C, then determine the angle between vec A and ve...

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  16. For two vectors vec(A) and vec(B) if vec(A) + vec(B) = vec(C) and A +B...

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  17. Prove that (vec(A) +2vec(B)) .(2vec(A) - 3vec(B)) = 2A^(2) +AB cos the...

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  18. Prove that the vectors vec(A) = 4 hati +3hatj +hatk and vec(B) = 12 ha...

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  19. If vec(A) = 2hati +3 hatj +hatk and vec(B) = 3hati + 2hatj + 4hatk, th...

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  20. Find the value of a for which the vectors 3 hati + 3hatj + 9 hatk and ...

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