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If (veca + vecb).(veca-vecb) = 0 show th...

If `(veca + vecb).(veca-vecb)` = 0 show that `|veca|` = `|vecb|`.

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`(veca+vecb).(veca-vecb) = 0`
`implies veca.(veca-vecb)+vecb(veca-vecb) = 0`
[because Dot product is distributed over vector addition.]
`implies veca.veca-veca.vecb+vecb.veca-vecb.vecb = 0`
`implies veca.veca-vecb.vecb = 0 [because vecavecb = vecb.veca = 0]`
`implies |veca|^2 = |vecb|^2 implies |veca| = |vecb|` (Proved)
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MBD PUBLICATION-VECTORS-QUESTION BANK
  1. In each of the problems given below, find the work done by a force vec...

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  2. In each of the problems given below, find the work done by a force vec...

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  3. If (veca + vecb).(veca-vecb) = 0 show that |veca| = |vecb|.

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  4. If a and b are perpendicular vectors show that (veca+vecb)^2 = (veca-v...

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  5. Prove that two vactors are perpendicular iff |veca+vecb|^2 = |veca|^...

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  6. If veca, vecb, vecc are mutually perpendicular vectors of equal magnit...

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  7. Prove the following by vector method. Altitudes of a triangle are conc...

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  8. Prove the following by vector method. Median to the base of an isoscel...

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  9. Prove the following by vector method. The parallelogram whose diagonal...

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  10. Prove the following by vector method. The diagonals of a rhombus are a...

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  11. Prove the following by vector method. An angle inscribed in a semi-cir...

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  12. Prove the following by vector method. in any triangle ABC, a = bcosC...

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  13. Prove the following by vector method. In a triangle AOB, mangleAOB = 9...

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  14. Prove the following by vector method. Measure of the angle between two...

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

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  16. A vector perpendicular to the vectors hati+hatj and hati+hatk is

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  17. The area of the triangle with vertices (1,0,0), (0,1,0) and (0,0,1) is

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  18. If veca and vecb are unit vectors such that vecaxxvecb is a unit vecto...

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  19. If veca, vecb and vecc are non-zero vectors, then vecaxxvecb = vecaxxv...

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  20. Let veca = 2hati+hatj, vecb = -hati+3hatj+hatk and vecc = hati+2hatj+...

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