The length of line segment joining the points with position vectors \(2\hat{\imath}-2\hat{\jmath}+3\hat{k}\) and \(5\hat{\imath}+2\hat{\jmath}+3\hat{k}\) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 5
Let the points be P and Q. The vector \(\overrightarrow{PQ}\) is the difference of the position vectors:
\(\overrightarrow{PQ} = (5 - 2)\hat{\imath} + (2 + 2)\hat{\jmath} + (3 - 3)\hat{k} = 3\hat{\imath} + 4\hat{\jmath}\)
Its magnitude is the length of the segment:
\(PQ = \sqrt{3^2 + 4^2 + 0^2} = \sqrt{25} = 5\)