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show that (vecaxxvecb)xxvecc=vecaxx(vecb...

show that `(vecaxxvecb)xxvecc=vecaxx(vecbxxvecc)` if and only if `veca and vecc` are collinear or `(vecaxxvecc)xxvecbxxvec0`

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we are given that
`(veca.vecc) vecb-(vecb.vecc)veca=(veca.vecc)vecb - (veca.vecb) vecc`
`(veca.vecb)vecc-(vecb.vecc)veca=vec0`
`Rightarrow (vecaxxvecc) xxvecb=vec0`
Thus , either , `vecb =vec0 or veca xx vecc = vec0`
But `vecb ne vec0` therefore, `veca xx vecc =vec0` and hence
`vecc = t veca ,, i.e. veca and vecc` are collinear.
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CENGAGE-DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS -Exercise
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  2. If veca and vecb be two non-collinear unit vectors such that vecaxx(ve...

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  3. show that (vecaxxvecb)xxvecc=vecaxx(vecbxxvecc) if and only if veca a...

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

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  5. If vecp, vecq , vecr denote vectors vecbxxvecc, vecc xx vecc xx veca, ...

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

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

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  8. vec a , vec b ,a n d vec c are three unit vectors and every two are...

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  9. 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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  10. If |{:((a-x)^(2),(a-y)^(2),(a-z)^(2)),((b-x)^(2),(b-y)^(2),(b-z)^(2)),...

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  11. OABC is a tetrahedron where O is the origin and A,B,C have position ve...

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  12. Let k be the length of any edge of a regular tetrahedron (a tetrahe...

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  13. In A B C , a point P is taken on A B such that A P//B P=1//3 and poin...

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  14. Let O be an interior point of DeltaABC such that bar(OA)+2bar(OB) + ...

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  15. The lengths of two opposite edges of a tetrahedron of aa n db ; the...

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  16. Find the volume of a parallelopiped having three coterminus vectors of...

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  17. Let vecp and vecq any two othogonal vectors of equal magnitude 4 each....

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  18. Given that vecA,vecB,vecC form triangle such that vecA=vecB+vecC. Find...

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  19. A line l is passing through the point vecb and is parallel to vector v...

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  20. If vec e1, vec e2, vec e3a n d vec E1, vec E2, vec E3 are two sets of...

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