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If vecx.veca=0 , vecx.vecb=0 , vec...

If ` vecx.veca=0 ` , ` vecx.vecb=0 ` , ` vecx.vecc=0 ` and ` vecxnevec0 ` then show yhat ` veca ` , ` vecb ` , ` vecc ` are coplanar .

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Since, `vecx` is a non-zero vectors, the given conditions will be satisfied if eitherm (i) vectors, `veca , vecb and vecc` are zero or (ii) `vecx` is perpendicular to vectors, `veca, vecb and vecc`.
in case (ii) `veca , vecb and vecc` are coplanar and so `[veca vecb vecc] =0`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
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  3. If vecx.veca=0 , vecx.vecb=0 , vecx.vecc=0 and vecxnevec0 ...

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

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

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

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

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

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  11. Let veca,vecb and vecc be the non zero vectors such that (vecaxxvecb)x...

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  12. If vec p , vec q , vec r denote vector vec bxx vec c , vec cxx vec a...

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  13. Let veca, vecb , vecc be non -coplanar vectors and let equations veca'...

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  14. Given unit vectors hatm hatn and hatp such that angle between hatm and...

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  15. Let vec a , vec b ,a n d vec c be non-coplanar unit vectors, equal...

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  16. Let veca=a(1)hati+a(2)hatj+a(3)hatk,vecb=b(1)hati + b(2)hatj + b(3)hat...

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  17. If |(a-x)^2(a-y)^2(a-z)^2(b-x)^2(b-y)^2(b-z)^2(c-x)^2(c-y)^2(c-a)^2|=0...

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  19. Prove that the smaller angle between any two diagonals of a cube is co...

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