A vector of magnitude `10 N` acting in X-Y-plane has componets `8 N` and `6 N` along positive X-axis and positive Y-axis, repectively.The coordinate system is rotated about Z-axis through angle `90^(@)` in anti-clockwise direction. Find x-components and y-component in new coordinate system.

Options

A. `F_(x)= 8 N, F_(y)= 6N`
B. `F_(x) = 6 N, F_(y)= 8N`
C. `F_(x)= 6N, F_(y)= -8 N`
D. `F_(x)= 0N, F_(y)= 10N`

Answer

C

Explanation

In new coordinates system,

`F sin 37^(@)= 6N`
`F cos 37^(@)= 8N`
x-component `F_(x)= F sin 37^(@)= 10xx3/5= 6N`

y-component `F_(y)= -F cos 37^(@)`
`= -10xx4/5= -8N`