Let p, q, r and s be respectively the magnitudes of the vectors `3hat(i)-2hat(j), 2 hat(i)+ 2hat(j)+hat(k), 4 hat(i)-hat(j)+hat(k), 2hat(i)+2hat(j)+3hat(k)`. Which one of the following is correct?

Options

A. `rgtsgtqgtp`
B. `sgtrgtpgtq`
C. `rgtsgtpgtq`
D. `sgtrgtqgtp`

Answer

C

Explanation

Let p = Magnitude of `3hat(i)-2hat(j)=sqrt(9+4)=sqrt(13)`
q = Magnitude of `2hat(i)+hat(j)+hat(k)=sqrt(4+4+1)=3`
r = Magnitude of `4hat(i)-hat(j)+hat(k)=sqrt(16+1+1)=sqrt(18)=3sqrt(2)`
s = Magnitude of `2hat(i)+2hat(j)+3hat(k)=sqrt(4+4+9)=sqrt(17)`
`:. r gt s gt p gt q`