The maximum and minimum magnitude of the resultant of two given vectors are 17 units and 7 unit respectively. If these two vectors are at right angles to each other, the magnitude of their resultant is

Options

A. 14
B. 16
C. 18
D. 13

Answer

D

Explanation

`R_("max")=A+B=17`, When `theta=0^(@)`
`R_("min")=A-B=7`, When `theta=180^(@) `
By solving we get `A=12 and B=5`
Now , when `theta=90^(@)`, then
`R=sqrt(A^2+B^2)`
`R=sqrt((12)^2+(5)^2)=sqrt(169)=13`