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If vecaxxvecb = vecbxxvecc ne vec0, prov...

If `vecaxxvecb = vecbxxvecc ne vec0`, prove that `veca+vecc = mvecb`, where m is a scalar.

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`vecaxxvecb = vecbxxvecc ne vec0`
`implies vecaxxvecb-vecbxxvecc = vec0`
`implies vecaxxvecb+veccxxvecb = vec0[because vecbxxvecc = -veccxxvecb]`
`implies (veca+vecc)xxvecb = vec0`
`implies veca+vecc` is parallel to `vecb`
`implies veca+vecc = mvecb` for some scalar m. (Proved)
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MBD PUBLICATION-VECTORS-QUESTION BANK
  1. Determine the sine of the angle between the vectors hat-3hatj+hatk, ha...

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  2. Show that (vecaxxvecb)^2 = a^2b^2 - (veca.vecb)^2.

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  3. If vecaxxvecb = vecbxxvecc ne vec0, prove that veca+vecc = mvecb, wher...

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  4. if vec = 2hati+hatj-hatk, vecb = -hati+2hatj-4hatk, vecc = hati+hatj+h...

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  5. If veca = 3hati+hatj-2hatk, vecb = 2hati-3hatj+4hatk then verify that ...

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  6. Find the area of the parallelogram whose diagonals are vectors 3hati+h...

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  7. Show that (veca-vecb)xx(veca+vecb) = 2(vecaxxvecb). Interpret this res...

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  8. Each question given below has four possible answers out of which only ...

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  9. (-veca).vecbxx(-vecc)) =

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  10. For the non-zero vectors veca, vecb and vecc, veca.(vecbxxvecc) = 0 if

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  11. Find the scalar triple product vecb.(veccxxveca) where veca, vecb and ...

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  12. Find the scalar triple product vecb.(veccxxveca) where veca, vecb and ...

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  13. Find the volume of the parallelopiped whose sides are given by the vec...

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  14. Find the volume of the Parallelepiped whose sides are given by the vec...

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  15. Show that the following vector are co-planar. hati-2hatj+2hatk, 3hati+...

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  16. Show that the following vector are co-planar. hati+2hatj+3hatk, -2hati...

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  17. Find the value of lambda so that the three vectors are co-planar. hati...

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  18. Find the value of lambda so that the three vectors are co-planar. (2,-...

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  19. If veca, vecb and vecc mutually perpendiculars, show that [veca.(vecbx...

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  20. Show that [veca+vecbvecb+veccvecc+veca] = 2[vecavecbvecc]

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