Solve : $p\vec x+\vec{x}(\vec{x}\cdot \vec{b})=\vec{a}\times \vec{b}+\vec{c}$.

Question

Prob: Solve : $p\vec x+\vec{x}(\vec{x}\cdot \vec{b})=\vec{a}\times \vec{b}+\vec{c}$.

I could not understand how to calculate it to solve the equation for $\vec x$.

Answer 1

First multiply by $b$ and notice that $(a\times b)\cdot b=0$. You'll get a quadratic equation for $x\cdot b$. Plug the solution in the original equation and solve for $x$.