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If the resultant of three forces vecF1= ...

If the resultant of three forces `vecF_1= phati +3hatj-hatk , vecF_2 =-5hati+hatj+2hatk and vecF_3= 6hati -hatk` acting on a particle has a magnitude equal to 5 units, then what is difference in the values of `p` ?

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The correct Answer is:
6
Let `vecR` be the resultant. Then
`" " vecR= vecF_1 + vecF_2 + vecF_3 = (p+1)hati +4hatj`
Given, `|vecR| = 5`, therefore `R^(2)= 25`
`because (p+1)^(2) + 16 = 25 or p +1 = pm3`
or `p =2, -4`
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