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If the vertices A, B, C of a triangle AB...

If the vertices A, B, C of a triangle ABC are (1,2,3), (-1,0,0), (0,1,2) respectively, then find `angleABC` [ `angleABC` is the angle between the vectors `vec(BA)` and `vec(BC)` ]

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MODERN PUBLICATION-VECTORS-Exercise
  1. If veca,vecb,vecc are unit vectors such that veca+vecb+vecc=vec0, find...

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  2. If either vector veca=vec0 or vecb=vec0, then veca*vecb=vec0. But the ...

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

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

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  5. Using vector method, show that the points whose position vectors are ,...

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  6. If veca is a nonzero vector of magnitude 'a' and lambda a nonzero s...

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  7. Find |vecaxxvecb| if veca=hati-7hatj+7hatk and vceb=3hati-2hatj+2hatk.

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  8. Find a unit vector perpendicular to each of the vector veca + vecb and...

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  9. If a unit vector veca, makes angles pi/3with hati, pi/4wih hatj and...

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  10. Show that (veca-vecb)xx(veca+vecb)=2(vecaxxvecb).

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  11. Find lambda and mu if : (2hati+6hatj+27hatk)xx(hati+lambdahatj+muhatk)...

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  12. Given that veca cdot vecb = 0 and vecaxxvecb = vec0. What can you conc...

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  13. Let the vectors veca,vecb,vecc be given as : a1hati+a2hatj+a3hatk,b1ha...

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  14. If either veca = vec0or vecb = vec0 then vecaxxvecb= vec0. Is the con...

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  15. Find the area of the triangle with vertices A(1,12), B(2,3,5), C(1,5,5...

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  16. Determine the area of a parallelogram whose adjacent sides are represe...

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  17. Let the vectors veca and vecb be such that |veca| = 3 and |vecb| = sqr...

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  18. Area of a rectangle having vertices A, B, C and D with position vector...

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  19. Write down a unit vector in XY-plane, making an angle of 30^o with the...

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  20. Find the scalar components and magnitude of the vector joining the poi...

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