T1W7L3

#ae#specialist#vectors

alternate method (continued from last lesson) §

measure each angle anti-clockwise from the east.

• the advantages of this is that you don’t have to account for positives and negatives.

unit vector §

• given a vector $v$, the unit vector in the direction of $v$ has magnitude 1.
• the unit vector of $v$ points in the same direction of $v$ but has a magnitude of 1.
• the unit vector of $v$ is $\frac{1}{|v|}v$

• notation §

• for vector $v$ of magnitude $|v|$,
• $\vec{\hat{v}}=\frac{1}{|v|}v$

• why? §

• if we have a bunch of vectors in same direction, we can represent the multiple vectors without having to state it’s direction, and express those vectors as a scaled of $v$.

vector equations §

• vector questions can involve setting up equations and solving them.
• remember the two vectors are equal if and only if magnitude AND direction are equal.
• two vectors in component form are equal if and only if their components are equal.
• $ai+bj=ci+dj$ if and only if $a=c$ and $b=d$
• this means that solving equations with vectors in component form usually involves equating components.

typical question §

• airports A and B are such that $\overrightarrow{AB}=(600i+200j)km$. An aircraft is flown directly from A to B. The aircraft can maintain a steady speed of 390km/h in still air. There isa wind blowing with velocity (30i-20j) km/h.
• Find in the form ai + bj, the velocity vector the pilot should set so that this velocity, together with the wind, causes the lane to travel directly from A to B.

when drawing vectors §

• when drawing vectors, don’t miss velocity and displacement vectors, make the velocity smaller than the direction (this is crucial in the way you set out the experiment.)
• $\lambda$ to show that it is scaled.
• $ai+bj+30i-20j=\lambda 600i+\lambda 200j$
• $a+30=\lambda 600$ and $b-20=\lambda 200$
• we cant solve it with 3 variables in 2 equations
  • it most likely a calculate assumed, so use CAS to solve :D
  • $a+30=\lambda 600$
  • $b-20=\lambda 200$
  • $a^2+b^2=390^2$