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Show that the points A, B and C with pos...

Show that the points A, B and C with position vectors, `vec a= 3hat i-4 hatj -4 hat k, vec b= 2 hat i -hatj +hat k` and `vec c =hat i-3hat j-5 hat k`, respectively, form the vertices of a right angled triangle.

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PRADEEP PUBLICATION-VECTORS-EXERCISE
  1. Find the position vector of a point R which divides the line joining t...

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  2. Find the position vector of the mid-point of the vector joining the po...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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