The vectors a and b are unit vectors that make an angle of 60 degree with each other. If a-3b and ma+b are perpendicular, determine the value of m.

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If two vectors are unit vecors

`hata*hatb=cos(theta)=cos(60^o)=1/2 `

`hata*hata=1` and   `hatb*hatb=1`

So `(hata-3hatb)*(mhata+hatb)=mhata*hata-3hatb*mhata+hata*hatb-3hatb*hatb`

Simplifying we get `m(1)-3m(cos(theta))+cos(theta)-3(1)=m-(3m)/2+1/2-3=0`

This gives `-m/2-5/2=0` or `m = -5`

So `m = -5` is our answer.

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