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If a vector makes angles alpha,beta,gamm...

If a vector makes angles `alpha,beta,gamma. with . OX ,O Ya n dO Z` respectively, prove that `sin^2alpha+sin^2beta+sin^2gamma=2.`

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RD SHARMA ENGLISH-ALGEBRA OF VECTORS-All Questions
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  2. A vector vec O P is inclined to O X at 50^0 and O Y at 60^0 . Find th...

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  3. If a vector makes angles alpha,beta,gamma. with . OX ,O Ya n dO Z ...

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  4. A B C D is a parallelogram. If L and M are the mid-points of B C and D...

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  5. Find a unit vector in the direction of the resultant of the vectors...

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  6. Find the position vector of the mid-point of the vector joining the...

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  7. Show that the line joining one vertex of a parallelogram to the mid...

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  8. Let vec a , vec b, vec c be three non-zero vectors such that any two ...

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  9. If vec a , vec b are the position vectors of the points (1,-1),(-2,m...

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  10. Find the position vector of a point A in space such that vec O A is i...

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  11. Show that the points A(6,-7,0),B(16 ,-19 ,-4),C(0,3,-6)a n d D(2,-5,1...

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  12. Prove that the lines joining the vertices of a tetrahedron to the ce...

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  13. Find a vector vec r of magnitude 3sqrt(2)u n i t s which makes an an...

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  14. Let vec a= hat i+2 hat ja n d vec b=2 hat i+ hat jdoti s |vec a|=| ve...

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  15. Three vectors of magnitude a ,2a ,3a meet in a point and their directi...

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  16. Show that the vectors vec a-2 vec b+3 vec c , vec a-3 vec b+5 vec ca ...

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  17. Find the angles at which the vector 2 hat i- hat j+2 hat k is inclined...

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  18. Prove that four points 2 vec a+3 vec b- vec c , vec a-2 vec b+3 vec ...

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  19. Find the direction cosines of the vector joining the points A(1,2,-...

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  20. If vec aa n d vec b are two non-collinear vectors, show that points...

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