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

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

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For what value of a are the vectors vec(A) = a hati - 2hatj +hatk and vec(B) = 2a hati +a hat j - 4hatk perpendicular to each other ?

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

What is the value of a, if two vectors vec P =hati+12 hatj+hatk and vec Q =2hati-ahatj+4hatk are perpendicular to each other ?

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If vector vecP=a hati + a hatj +3hatk and vecQ=a hati -2 hatj -hatk are perpendicular to each other , then the positive value of a is

For what value of lamda are the vectors veca=2hati+lamda hatj+hatk and vecb=hati-2hatj+3hatk perpendicular to each other ?

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SL ARORA-Motion in a Plane-Example
  1. Two billiard balls are rolling on a flat table. One has the velocity c...

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

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

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  4. Two vector vec A = 5hati+7hatj-3hatk and vec B=2hati+2hatj-alphahatk a...

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  5. If the magnitudes of two vectors are 3 and 4 and their scalar product ...

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  6. A body constrained to move along the z-axis of a co-ordinate system is...

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  7. A force of 7 hati+ 6 hatk newton makes a body move on a rough plane wi...

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  8. Three vectors vec(A),vec(B) and vec(C) are such that vec(A) = vec(B)+v...

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  9. If |vec A + vec B|=|vec A-vecB|, finf the angle between vec A and vec ...

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  10. If vector P, Q and R have magnitude 5,12,and 13 units and vec(P)+vec(Q...

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  11. Determine the angles which the vector vec(A) = 5 hati + 0 hatj +5hat...

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

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

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

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

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

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

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

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

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

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