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If vec a, vec b, vec c are unit vectors ...

If `vec a, vec b, vec c` are unit vectors such that `vec a+ vec b+ vec c =0`, find the value of `vec a.vec b+ vec b .vec c + vec c. vec a`.

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Clearly, `veca , vecb and vecc` respesent the sides of a tirangle,
`Rightarrow veca xx vecb =vecc xx veca `
`or veca xxvecb + vecc + vecb xx vecc xx veca = 3veca xx vecb`
`or 2vecb xx veca +vecb xx vecc + vecc xx veca = 0 Rightarrow lambda=2`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. If vec x and vecy are unit vectors and |vecz| = 2/sqrt7 such that vecz...

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  2. prove that (veca.hati)(vecaxxhati)+(veca.hatj)(vecaxxhatj)+(veca.hatk)...

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  3. If vec a, vec b, vec c are unit vectors such that vec a+ vec b+ vec c ...

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  4. A particle has an angular speed of 3 rad/s and the axis of rotation...

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  5. If veca,vecb,vecc be unit vectors such that veca.vecb=veca.vecc=0 and ...

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  6. if (vecaxxvecb)^(2)+ (veca.vecb)^(2) = 144 and |veca|=4 the find the v...

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  7. Given |veca|=|vecb|=1 and |veca + vecb|= sqrt3 "if" vecc is a vector s...

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  8. Find the moment of vec F about point (2, -1, 3), where force vec ...

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  9. If veca , vecb , vecc and vecd are four non-coplanar unit vectors such...

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  10. If vectors veca, vecb and vecc are coplanar, show that |{:(veca, vecb,...

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  11. If the volume of a parallelepiped whose adjacent edges are vec a=2...

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  12. If veca=hati+hatj+hatk and vecb = hati-2hatj+hatk then find vector vec...

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  13. If vecx.veca=0 , vecx.vecb=0 , vecx.vecc=0 and vecxnevec0 ...

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  14. If veca=hati+hatj+hatk and vecb = hati-2hatj+hatk then find vector vec...

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  15. If veca , vecb and vecc are three vectors such that vecaxx vecb =vecc...

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  16. If veca= vecP + vecq, vecP xx vecb = vec0 and vecq. vecb =0 then prove...

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  17. prove that (veca.(vecbxxhati))hati+(veca.(vecbxxhatj))hatj+ (veca.(vec...

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  18. for any four vectors veca,vecb, vecc and vecd prove that vecd. (vecax...

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  19. If veca and vecb be two non-collinear unit vectors such that vecaxx(ve...

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  20. If vecaxx(vecbxxvecc)=(vecaxxvecb)xxvecc for non coplanar veca,vecb,v...

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