If x, y are non-zero vectors with | x+ y|=| x|, and 2 x+ y is perpendicular to y, then is …

Question

If $\vec x,\vec y$ are non-zero vectors with $|\vec x+\vec y|=|\vec x|$, and $2\vec x+\lambda\vec y$ is perpendicular to $\vec y$, then $\lambda$ is \_\_\_\_\_\_\_.

Answer: 1

Accepted Answer

$(2\vec x+\lambda\vec y)\cdot\vec y=0 \Rightarrow 2\vec x\cdot\vec y+\lambda|\vec y|^2=0$ \ldots  (ii)

Comparing (i),(ii): $\lambda=1$.

Solutions · 1