The length of line segment joining the points with position vectors $2\hat i-2\hat j +3\hat k$ and $5\hat i +2\hat j +3\hat k$ is

5

The correct answer is Option (4) → 5

Position vectors are $\vec a=(2,-2,3)$ and $\vec b=(5,2,3)$.

Vector joining the points:

$\vec b-\vec a=(5-2,\;2-(-2),\;3-3)=(3,4,0)$

Length of the line segment:

$|\vec b-\vec a|=\sqrt{3^{2}+4^{2}+0^{2}}$

$=\sqrt{9+16}=5$

Final answer: $5$