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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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The correct Answer is:
1
` vecX. vecA = 0 Rightarrow " either " vecA = 0 or vecX bot vecA`
` vecX.vecC =0 Rightarrow " either" vecC=0 vecX bot vecC`
In any of the three cases,
`vecA, vecB, vecC =0 Rightarrow [vecA vecB vecC] =0`
Otherwise if `vecX bot vecA, vecX bot vecB and vecX bot vecC` , then
`vecA, vecB and vecC` are coplanar. then
` [ vecA vecB vecC] =0`
Therefore, the statement is true.
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
  1. If veca = hatj + sqrt3hatk vecb= - hatj + sqrt3 hatk and vecc = 2sqrt3...

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

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

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  4. for any three vectors, veca, vecb and vecc , (veca-vecb) . (vecb -vecc...

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  5. The scalar vecA.(vecB+vecC)xx(vecA+vecB+vecC) equals (A) 0 (B) [vecA v...

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  6. For non zero vectors veca,vecb, vecc |(vecaxxvecb).vecc|=|veca||vecb...

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  7. The volume of he parallelepiped whose sides are given by vec O A=2...

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  8. If veca , vecb , vecc are three non-coplanar vector and vecp...

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  9. Let veca=hati-hatj, vecb=hatj-hatk, vecc=hatk-hati. If hatd is a unit ...

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  10. If veca, vecb, vecc are three non - coplanar vector such that vecaxx(v...

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  11. Let vecu, vecv and vecw be vector such that vecu+vecv+vecw=vec0. If |v...

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  12. If veca, vecb and vecc1 are three non-coplanar vectors, then (veca + v...

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  13. vec p , vec q ,a n d vec r are three mutually perpendicular vectors of...

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  14. Let veca=2vecj+vecj-2veck,vecb=veci+vecj. If vecc is a vector such tha...

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  15. Let vec a=2i+j+k , vec b=i+2j-k and a unit vector vec c be coplanar....

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  16. If the vectors veca,vecb,vecc form the sides BC,CA and AB respectively...

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  17. Consider the vectors, vec(a),vec(b),vec(c),vec(d) such that (vec(a)xxv...

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  18. If veca, vecb and vecc are unit coplanar vectors , then the scalar tri...

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  19. If hat a , hat b ,a n d hat c are unit vectors, then | hat a- hat b|^...

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  20. If veca and vecb are two unit vectors such that veca+2vecb and 5veca-4...

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