Every Whole number is Natural number?

Answer

C, D

Explanation

Let a,b and c lie in the XY-plane
Let `a=hati,b=-(1)/(2)hati+(sqrt(3))/(2)hatj and c=-(1)/(2)hati-(sqrt(3))/(2)hatj`
Therefore, `|p+q+r|=|lamda a+mub+vc|`
`=|lamdahati+mu(-(1)/(2)hati+(sqrt(3))/(2)hatj)+v(-(1)/(2)hati-(sqrt(3))/(2)hatj)|`
`|(lamda+(mu)/(2)-(v)/(2))hati+(sqrt(3))/(2)(mu-v)hatj|`
`=sqrt((lamda-(mu)/(2)-(v)/(2))^(2)+(3)/(4)(mu-v)^(2))`
`=sqrt(lamda^(2)+mu^(2)+v^(2)-lamdamu-lamdav-muv)`
`=(1)/(sqrt(2))sqrt((lamda-mu)^(2)+(mu-v)^(2)+(v-lamda)^(2))`
`=(1)/(sqrt(2))sqrt(1+1+4)=sqrt(3)`.