In a two diamensional motion of a particle, the particle moves from point A, with position vector `vec(r )_(1)` to point B, with position vector `vec(r )_(2)`. If the magnitudes of these vectors are, respectively, `r_(1)=3` and `r_(2)=4` and the angles they make with the x-axis are `theta_(1)=75^(@)` and `theta_(2)=15^(@)`, respectively, then find the magnitude of the displacement vector. `

Options

A. 15
B. `sqrt(13)`
C. 17
D. `sqrt(15)`

Answer

B

Explanation

Displacement `=vec(AB)`, angle between `vec(r )_(1)` and `vec(r )_(2)` is `theta = 75^(@)-15^(@)=60^(@)`
From (Figure), `AB^(2)=r_(1)^(2)+r_(2)^(2)-2r_(1)r_(2)cos theta`
`=3^(2)+4^(2)-2xx3xx4cos 60^(@)=13`
`rArr AB=sqrt(13)`