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Let veca=hati+hatj+hatk,vecb=2hati+3hatk...

Let `veca=hati+hatj+hatk,vecb=2hati+3hatk,vecc=hati-hatj` and `vecd=6hati+2hatj+3hatk`. If `vecd=x(vecbxxvecc)+y(veccxxveca)+z(vecaxxvecb)` where x, y and z are scalars then the value of `x+y+z` is k. the number of prime factors of 5k is.

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The correct Answer is:
2
`veca.vecd=x[vecavecbvecc]`
`x=(veca.vecd)/([vecavecbvecc]),y=(vecbvecd)/([vecavecbvecc]),z=(veccvecd)/([vecavecbvecc])`
`((veca+vecb+vecc).vecd)/([vecavecbvecc])=(34)/(5)`
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