1 Chalkboard
Figure 1: Review of dot product
Figure 2: Components of \(\vec{A}\) along direction \(\vec{u}\)
Figure 3: Pendulum problem with projections
2 Which is it the angle between 2 vectors?
2.1 Front
Which is it the angle between 2 vectors?
2.2 Back
\({\displaystyle \cos \theta = \frac{\vb{A} \cdot \vb{B}}{\abs{\vb{A}} \abs{\vb{B}}}}\)
3 Which is the vector rotated \(\SI{90}{\degree}\) counter-clockwise?
3.1 Front
Which is the vector rotated $\SI{90}{\degree}$ counter-clockwise?
\(\vb{A} = \ev{a_1, a_2}\)
3.2 Back
\(\ev{-a_2, a_1}\)
4 How we can know which kind of angle there is between 2 vectors?
4.1 Front
How we can know which kind of angle there is between 2 vectors?
- Acute, right or obtuse
4.2 Back
- \({\displaystyle \cos \theta = \frac{\vb{A} \cdot \vb{B}}{\abs{\vb{A}} \abs{\vb{B}}}}\)
- Numerator can say if there is positive or negative, if it’s negative it’s obtuse because of \(\cos (\theta)< 0\) when \(\theta > \pi/2\).
- We will need to check if \(\vb{A} \cdot \vb{B} = 0\), \(\vb{A} \cdot \vb{B} = \abs{\vb{A}} \abs{\vb{B}}\)
5 Which is the components of \(\vb{A}\) along direction \(\hat{u}\)?
5.1 Front
Which is the components of $\vb{A}$ along direction $\hat{u}$?
5.2 Back
- \(\abs{\hat{u}} = 1\)
