Let a, b, c be unit vectors with | a- b|^2+| a- c|^2=8.

Question

Answer: 2

Accepted Answer

Expanding: $2-2\vec a\cdot\vec b+2-2\vec a\cdot\vec c=8 \implies \vec a\cdot\vec b+\vec a\cdot\vec c=-2$

$$|\vec a+2\vec b|^2+|\vec a+2\vec c|^2 = 1+4+4\vec a\cdot\vec b+1+4+4\vec a\cdot\vec c = 10+4(-2)=2$$

Solutions · 1