If the extremities (end points) of a diagonal of a square are `(1,-2,3) and (2,-3,5)` then find the length of the side of square.

Options

A. `sqrt(6)`
B. `sqrt(3)`
C. `sqrt(5)`
D. `sqrt(7)`

Answer

B

Explanation

Let `P(1,-2,3)` and `R(2-3,5)` be the coordinates of the extremities `P` and `R` of a diagonal of the square `PQRS` then
`PR=sqrt((2-1)^(2)+(-3+2)^(2)+(5-3)^(2))=sqrt(6)`
`:.` Length of the side `=(sqrt(6))/(sqrt(2))=sqrt(3)` [ Diagonal `=sqrt(2)` (side)]