Question

find d/dt (F-G) if if F(t) = 4t^2i - tj + t^2k and G(t) = ti + 2t^2j + 4 sin t k

Answer 1

$$\vec F(t) = 4t^2\vec i - t\vec j + t^2\vec k$$

$$\vec G(t) = t\vec i + 2t^2\vec j + 4 \sin t\vec k$$

$$\vec F(t)-\vec G(t) = (4t^2-t)\vec i +(-t-2t^2)\vec j +( t^2-4\sin t)\vec k$$

$$\dfrac{d}{dt}(\vec F-\vec G)=(8t-1)\vec i +$$

$$+(-1-4t)\vec j +( 2t-4\cos t)\vec k$$