Determine coefficient λ so vectors p and q are mutually perpendicular

Question

p=λa+17b

q=3a-b

|a|=2 , |b|=5 , angle between a & b vector is 120°

I got for vectors a and b

$$ \vec{a}=(-1,\sqrt{3}) \vec{b}=(\frac{-5}{2},\tfrac{5\sqrt{3}}{2})\ $$

how do I find coefficient λ ?

Answer 1

Hint: we get $$\vec{p}\cdot \vec{q}=3\lambda\vec{a}^2+51\vec{a}\cdot \vec{b}-\lambda\vec{a}\cdot \vec{b}-17\vec{b}^2$$ and use that $$\vec{x}^2=|\vec{x}|^2$$