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Consider the vectors hat i+cos(beta-alp...

Consider the vectors ` hat i+cos(beta-alpha) hat j+cos(gamma-alpha) hat k ,cos(alpha-beta) hat i+ hat j+"cos"(gamma-beta) hat k` and `cos(alpha-gamma) hat i+cos(beta-gamma) hat j+a hat k `where `alpha,beta`, and `gamma` are different angles. If these vectors are coplanar, show that `a` is independent of `alpha,beta` and `gamma`

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CENGAGE PUBLICATION-VECTOR ALGEBRA-All Questions
  1. If points hat i+ hat j , hat i- hat j and p hat i+q hat j+r hat k are...

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  2. The position vector of the points P and Q are 5 hat i+7 hat j-2 hat ...

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  3. Consider the vectors hat i+cos(beta-alpha) hat j+cos(gamma-alpha) hat...

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  4. If vec A and vec B are two vectors and k any scalar quantity greater ...

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  5. The vectors x hat i+(x+1) hat j+(x+2) hat k ,(x+3) hat i+(x+4) hat j+(...

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  6. vec A isa vector with direction cosines cosalpha,cosbetaa n dcosgammad...

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  7. A vector oversetrarra has components 2p and 1 with respect to a rectan...

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  8. The sides of a parallelogram are 2 hat i+4 hat j-5 hat k and hat i+2 ...

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  9. If vec a , vec b , vec c are non-coplanar vector and lambda is a re...

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  10. If points hat i+ hat j , hat i- hat j and p hat i+q hat j+r hat k are...

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  11. If the vectors hat i- hat j , hat j+ hat k and vec a form a triangl...

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  12. If the resultant of three forces vec F1=p hat i+3 hat j- hat k , v...

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  13. If vec a, vec b, vec c are unit vectors satisfying the condition veca+...

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  14. The vector hat i+x hat j+3 hat k is rotated through an angle theta an...

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  15. Prove that point hat i +2 hat j - 3 hat k ,2 hat i - hat j + hat k ...

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  16. Show that the point A , B and C with position vectors vec a =3 hat i ...

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  17. If 2vec(AC)=3vec(CB), then prove that 2vec(OA)+3vec(OB)=5vec(OC) where...

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  18. Find the unit vector in the direction of vector vec (PQ), where P and...

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  19. For given vector, vec a = 2 hat i j +2 hat k and vec b = - hat i + ...

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  20. If the projections of vector vec a on x -, y - and z -axes are 2, ...

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