Maths vector algebra

Question

Given vec|a|=|b|=1 and vec|a+b|=√3 find c.b if c satisfies c-a-2b = 3(a×b).

Answer 1

We have \(\vec{c}-\vec{b}=\vec{a}-\vec{b}+2\)

\(|\vec{a}+\vec{b}|=\sqrt{\vec{a^2}+\vec{b^2}+2.\vec{b_3}}=1+1+2(\vec{a}.\vec{b})\)

\(\frac{1}{2}=\vec{a}-\vec{b}\)

\(\vec{c}-\vec{b}=\frac{5}{2}\)