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Show that the direction cosines of a vec...

Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are `(1/sqrt3), (1/sqrt3), (1/sqrt3)`

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

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  2. The two adjacent sides of a parallelogram are given by the vectors 2ha...

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  3. Show that the direction cosines of a vector equally inclined to the ax...

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  4. Let veca=hati+4hatj+2hatk,vecb=3hati-2hatj+7hatk and vecc=2hati-hatj+4...

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  5. The scalar product of the vector hati+hatj+hatk with a unit vector alo...

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  6. If veca, vecb, vecc are mutually perpendicular vectors of equal magnit...

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  7. Prove that (veca+vecb) cdot (veca+vecb) = |veca|^2 + |vecb|^2, if and ...

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  8. If theta is the angle between two vectors veca and vecb, then veca c...

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  9. Let veca and vecb be two unit vectors and theta is the angle between t...

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  10. The value of : hati*(hatjxxhatk)+hatj*(hatixxhatk)+hatk*(hatixxhatj) i...

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  11. If theta is the angle between two vectors veca and vecb, then |veca*ve...

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  12. Using vectors, find the value of 'k' such that the points (k,-10,3),(1...

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  13. If A,B,C,D are the points with position vectors : hati+hatj-hatk,2hati...

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  14. Parallelogram on equal bases and between the same parallels are equal ...

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  15. Write all the unit vectors in XY-plane.

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

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  17. Find a vector of magnitude 5 units, and parallel to the resultant of t...

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  18. If veca=hati+hatj+hatk,vecb=2hati-hatj+3hatk,vecc=hati-2hatj+hatk, the...

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  19. If veca=2hati-hatj+hatk,vecb=hati+3hatj-hatk,vecc=-2hati+hatj-3hatk an...

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  20. Show that the points A(1,-2,-8), B(5,0,-2) and C(11,3,7) are collinear...

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