hw1 review

ONCS Steps

• Normalize vector
• Normalize perpendicular vector
• 2 normalize: Take magnitude, divide each component by it
• 2 find perp of 2d vect: <a,b> = <b,-a> (normal → perp)

Describe $\vec{v}$ as linear sys of EQ

• in an oncs given some $\vec{v}$ and $\hat{a},\hat{b}$ (a and b are from ONCS)
• then $\vec{v}=(\vec{v}\cdot \hat{a})\hat{a}+(\vec{v}\cdot \hat{b})\hat{b}$
• Distance: $\frac{||\vec{v}\times w\stackrel{⃗}{}||}{magnitude}$

Rep $\vec{v}$ as linear combo of $\vec{a},\vec{b}$

• Take $\vec{a}=v_1$ and $\vec{b}=v_2$
• then can obtain a systems of eq, where $v_1=\vec{v}$‘s first component
• solve sys of eq to find for a&b: $\vec{v}=x\vec{a}+y\vec{b}$

IMPT: CONVERT BTWN 3 CORDS SYS

ed

Area of triangle degenerate? amex

• Take 2 vectors given all points $v_1{v}_2$
• take $\frac{1}{2}||\overrightarrow{v_1}\times \overrightarrow{v_2}||$ = area == 0 ? degen : !degen

Construct plane out of 3 pts

• Make 2 vectors given all points $v_1{v}_2$
• cross product (x,y,z)=1