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If the vectors vecalpha = a hati + hatj ...

If the vectors `vecalpha = a hati + hatj + hatk, vecbeta = hati + b hatj + hatk and vec gamma = hati + hatj + c hatk ` are coplanar, then prove that `(1)/(1-a ) +(1)/(1-b)+ (1)/(1-c)=1` where `a ne 1, b ne 1 and c ne 1`

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CBSE COMPLEMENTARY MATERIAL-VECTORS -FOUR MARKS QUESTIONS
  1. If veca = hati + hatj + hatk, vecc = hatj - hatk are given vectors, th...

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  2. Let, veca , vecb and vecc be three non zero vectors such that vecc is ...

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  3. If the vectors vecalpha = a hati + hatj + hatk, vecbeta = hati + b hat...

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  4. Find the altitude of a parallelepiped determined by the vectors veca, ...

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  5. Prove that the four points (4hati + 5 hatj+hatk), - (hatj +hatk),(3hat...

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  6. If |veca| =3, |vecb|=4 and |vecc|=5 such that each is perpendicular to...

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  7. Decompose the vector 6 hati - 3 hatj - 6 hatk into vectors which are p...

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  8. If veca, vecb and vecc are vectors such that veca. vecb = veca.vecc, v...

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  9. If veca, vecb and vecc are three non zero vectors such that veca xx v...

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  10. For any three vectors veca, vecb, vecc the value of [(veca-vecb, vecb-...

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  11. If [veca vecbvecc]=2 find the volume of the parallelepiped whose co-te...

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  12. If veca +vecb +vecc=0, |veca|=3,|vecb|=5, |vecc|=7 , then find the ang...

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  13. If the magnitude of the vector product of the vector hati+hatj+hatk wi...

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  14. If vecaxxvecb=veccxxvecd and vecaxxvecc=vecbxxvecd show that (veca-vec...

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  15. Find a vector of magnittude sqrt(171) which is perpendicular to both o...

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  16. If a is a nonzero real number prove that the vectors overset(r) alph...

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  17. If with reference to a right handed system of mutually perpendicula...

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  18. Find a unit vector perpendicular to plane ABC when position vectors of...

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  19. Find a unit vector in XY plane which makes an angle 45^(@) with the ve...

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  20. Suppose veca = lamda hati - 7 hatj + 3 hatk, vecb = lamda hati + hatj ...

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