Let a =2 i - j + k, b = i +2 j - k and c = i + j -2 k be three vectors. A vector of the type b +λ c for some scalar λ, whose projection on a is of…

Let $\displaystyle \overrightarrow{\mathrm{a}}=2 \hat{i}-\hat{j}+\hat{k}, \overrightarrow{\mathrm{~b}}=\hat{i}+2 \hat{j}-\hat{k}$ and $\displaystyle \vec{c}=\hat{i}+\hat{j}-2 \hat{k}$ be three vectors. A vector of the type $\displaystyle \vec{b}+\lambda \vec{c}$ for some scalar $\displaystyle \lambda$, whose projection on $\displaystyle \overrightarrow{\mathrm{a}}$ is of magnitude $\displaystyle \sqrt{\frac{2}{3}}$, is :