Two forces are acting on a same body `vec(F_(1))=(2hat(i)+3hat(j)-hat(k))` and `vec(F_(2))=(hat(i)+2hat(j)+4hat(k))`, then find component of `vec(F_(1))` along `vec(F_(2))`.

Options

A. `((4)/(7sqrt(6)))`
B. `(4)/(9sqrt(5))`
C. `(4)/(sqrt(21))`
D. `(7)/(4sqrt(6))`

Answer

C

Explanation

`vec(F_(1))implies2hat(i)+3hat(j)-hat(k)`
`vec(F_(2))implieshat(i)+2hat(j)+4hat(k)`
`F_(1)cos thetaimplies (vec(F_(1)).vec(F_(2)))/(|F_(2)|)implies(2+6-4)/(sqrt(21))implies(4)/(sqrt(21))`