Question

Find the derivative of the vector function
r(t) = ta X (b + tc)
(X is cross product)

Answer 1

To find the derivative of the vector function r(t) = ta X (b + tc), we need to take the derivative of each component of the function separately.

Step-by-step explanation:

To find the derivative of the vector function r(t) = ta X (b + tc), we need to take the derivative of each component of the function separately. Let's break it down: Derivative of x-component: The derivative of ta is a, and the derivative of b + tc is c. So, the derivative of the x-component is ac.

Derivative of y-component: The derivative of ta is a, and the derivative of b + tc is 0 since b is a constant. So, the derivative of the y-component is a x 0 = 0. Derivative of z-component: The derivative of ta is a, and the derivative of b + tc is c. So, the derivative of the z-component is ac.

Therefore, the derivative of the vector function r(t) = ta X (b + tc) is r'(t) = acî + 0ĵ + acḱ.