(1) (2a⃗+b⃗)⋅(a⃗−b⃗)=2∣a∣2−a⃗⋅b⃗−∣b∣2=8+3−9=2(2\vec{a}+\vec{b})\cdot(\vec{a}-\vec{b}) = 2|a|^2 - \vec{a}\cdot\vec{b} - |b|^2 = 8+3-9=2(2a+b)⋅(a−b)=2∣a∣2−a⋅b−∣b∣2=8+3−9=2 (2) ∣a⃗−2b⃗∣2=∣a∣2−4a⃗⋅b⃗+4∣b∣2=4+12+36=52|\vec{a}-2\vec{b}|^2 = |a|^2 - 4\vec{a}\cdot\vec{b}+4|b|^2 = 4+12+36=52∣a−2b∣2=∣a∣2−4a⋅b+4∣b∣2=4+12+36=52 (3) cosθ=a⃗⋅b⃗∣a⃗∣⋅∣b⃗∣=−32⋅3=−12θ=120°\cos\theta = \frac{\vec{a}\cdot\vec{b}}{|\vec{a}|\cdot|\vec{b}|} = \frac{-3}{2\cdot 3} = -\frac{1}{2} \qquad \theta = 120°cosθ=∣a∣⋅∣b∣a⋅b=2⋅3−3=−21θ=120° (4) ∣a⃗+b⃗∣=(a⃗+b⃗)2=∣a∣2+2a⃗⋅b⃗+∣b∣2=4−6+9=7|\vec{a}+\vec{b}| = \sqrt{(\vec{a}+\vec{b})^2} = \sqrt{|a|^2+2\vec{a}\cdot\vec{b}+|b|^2} = \sqrt{4-6+9} = \sqrt{7}∣a+b∣=(a+b)2=∣a∣2+2a⋅b+∣b∣2=4−6+9=7