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If vec a and vec b are two collinear vec...

If `vec a and vec b` are two collinear vectors then which of the following are incorrect :

A

`vec b =λ vec a`, for some scalar

B

`vec a = pm vecb`

C

the respective components of `vec a and vec b` are proportional

D

both the vectors `vec a and vec b` have same direction, but different magnitudes.

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PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Find the position vector of the mid-point of the vector joining the po...

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  2. Show that the points A, B and C with position vectors, vec a= 3hat i-4...

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  3. If vec a and vec b are two collinear vectors then which of the followi...

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  4. Find the angle between two vectors veca and vecb with magnitudes sqrt3...

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  5. Find the angle between the vectors hat i -2 hatj +3 hat k and 3 hat i ...

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  6. Find the projection of the vector hat i - hat j on the vector hat i +...

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  7. Find the projection of the vector hat i +3 hat j +7 hatk on the vector...

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  8. Show that each of the given three vectors is a unit vector : 1/7 (2 ha...

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  9. Find |vec a| and |vec b| lf(veca + vec b)*(vec a-vec b)=8 and |vec a |...

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  10. Evaluate the product (3 vec a-5 vec b)*(2 vec a+7 vec b).

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  11. Find the magnitude of two vectors veca and vecb, having the same magni...

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  12. If vec a =2 hat i + 2 hat j +3 hat k, vec b=-hat i + 2 hat j +hat k t...

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  13. Show that |vec a|vec b + |vec b|vec a perpendicular to |vec a|vec b - ...

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  14. If |a|=5,|a-b|=8 and |a+b|=10, then |b| is equal to

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  15. If vec a, vec b, vec c are unit vectors such that vec a+ vec b+ vec c ...

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  16. If either vector veca = 0or vecb = 0, then veca cdot vecb = 0.But the...

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  17. If the vertices A, B, C of a triangle ABC are (1,2,3), (-1,0,0), (0,1,...

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  18. Show that the points A(1,2,7), B(2,6,3) and C(3,10,-1) are collinear.

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  19. Show that the points A(2 hat i - hat j + hat k), B(hat i - 3 hat j- 5 ...

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  20. If vec a is a non-zero vector of magnitude ‘a’ and λ a non-zero scalar...

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