# Angles of a triangles whose $2$ sides are given by $2$ vectors

Let $$\hat{a}$$ be a unit vector and $$\vec{b}$$ be a non zero vector

not parallel to $$\hat{a}\;$$.Find the angles of a triangle,

two sides of which are represented by the vectors

$$\sqrt{3}(\hat{a}\times \vec{b})$$ and $$\vec{b}-(\hat{a}\cdot \vec{b})\hat{a}.$$

Try: Let $$\vec{p}=\sqrt{3}(\hat{a}\times \vec{b})$$ and $$\vec{q}=\vec{b}-(\hat{a}\cdot \vec{b})\hat{a}$$

So $$\vec{q}=(\hat{a}\cdot \hat{a})\vec{b}-(\hat{a}\cdot \vec{b})\hat{a}=-\hat{a}\times (\hat{a}\times \vec{b})$$

did not know how do i solve it , could some help me , Thanks

• We are not here to blindly answer your homework questions. Please explain the reasoning behind the steps you have tried and what techniques you have been taught about to solve these kind of problems – lioness99a Mar 1 at 12:03
• Have you tried using the Cauchy inequality? Use the dot product on P and Q and use the fact that that the dot product of orthogonal vectors will equal to zero. – Bor Kari Mar 1 at 12:54