I've watched Walter's third lecture in 8.01 and I have a small problem with the last part, where he says that $$\vec r_t=x_t\cdot \hat x\ +\ y_t\cdot \hat y\ +\ z_t\cdot \hat z \\ \vec v_t=\frac{d\vec r}{dt}=\dot x \hat x\ +\dot y \hat y\ +\dot z\hat z\\ \vec a_t=\frac{d\vec v}{dt}=\ddot x \hat x\ +\ddot y \hat y\ +\ddot z\hat z$$ and I have NO problem in understanding that, at least intuitively, but where can I find a resource to read about that in detail? I've flipped the entire Giancoli and Serway books and I can't find a single page on kinematics in 3D, the second chapter is always 1D with the third chapter talking about 2D but I can never find a chapter about 3D or at least any paper that talks about or that has the following formulae please help, if you can also give a rig. proof about those formulae, I'd be thankful

I've watched Walter's third lecture in 8.01 and I have a small problem with the last part, where he says that $$\vec r_t=x_t\cdot \hat x\ +\ y_t\cdot \hat y\ +\ z_t\cdot \hat z \\ \vec v_t=\frac{d\vec r}{dt}=\dot x \hat x\ +\dot y \hat y\ +\dot z\hat z\\ \vec a_t=\frac{d\vec v}{dt}=\ddot x \hat x\ +\ddot y \hat y\ +\ddot z\hat z$$ and I have NO problem in understanding that, at least intuitively, but where can I find a resource to read about that in detail? a book that's only prerequisite would be calculus 1, I need some exercises on that topic and I can't really find something like that in Giancoli