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if veca xx vecb = vecc,vecb xx vecc = ve...

if `veca xx vecb = vecc,vecb xx vecc = veca , " where " vecc ne vec0` then

A

`|veca|= |vecc|`

B

`|veca|= |vecb|`

C

`|vecb|=1`

D

`|veca|=vecb|= |vecc|=1`

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The correct Answer is:
a,c
`veca xx vecb = vecc, vecb xx vecc = veca`
taking cross with `vecb` in the first equation, we get
`vecb xx (veca xx vecb) = vecb xx vecc = veca `
`or |vecb|^(2) veca - (veca .vecb) vecb =veca`
` Rightarrow |vecb|=1 and veca.vecb=0`
Also `|veca xx vecb| = |vecc| or |veca| |vecb| sin (pi/2) = |vecc|`
`or |veca| = |vecc|`
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
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  2. Let veca and vecb be two non-collinear unit vectors. If vecu=veca-(vec...

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  3. if veca xx vecb = vecc,vecb xx vecc = veca , " where " vecc ne vec0 t...

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  4. Let veca, vecb, and vecc be three non- coplanar vectors and vecd be a ...

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  5. If veca, vecb and vecc are three unit vectors such that veca xx (vecb ...

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  6. If in triangle ABC, vec(AB) = vecu/|vecu|-vecv/|vecv| and vec(AC) = (...

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  7. [vecaxx vecb " " vecc xx vecd " " vecexx vecf] is equal to

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  8. The scalars l and m such that lveca + m vecb =vecc, " where " veca, ve...

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  9. If (veca xxvecb) xx (vecc xx vecd) . (veca xx vecd) =0 then which of t...

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  10. A,B C and dD are four points such that vec (AB) = m(2 hati - 6 hatj +...

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  11. about to only mathematics

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  12. Let vec(alpha)=ahati+bhatj+chatk, vec(beta)=bhati+chatj+ahatk and vec(...

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  13. If vectors vecA=2hati+3hatj+4hatk, vecB=hati+hatj+5hatk and vecC form ...

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  14. If veca=xhati + y hatj + zhatk, vecb= yhati + zhatj + xhatk and vecc= ...

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

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  16. A vector vecd is equally inclined to three vectors veca=hati-hatj+hatk...

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  17. A parallelogram is constructed on the vectors veca=3vecalpha-vecbeta, ...

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  18. Statement 1: Vector vecc = -5hati + 7 hatj + 2hatk is along the bisec...

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  19. Statement1: A component of vector vecb = 4hati + 2hatj + 3hatk in the ...

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  20. Statement 1: Distance of point D( 1,0,-1) from the plane of points A( ...

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