Let a = a_1 i + a_2 j + a_3 k a_i>0, i=1,2,3 be a vector which makes equal angles with the coordinate axes OX, OY and OZ. Also, let the projection of…

Let $\displaystyle \overrightarrow{\mathrm{a}}=\mathrm{a}_1 \hat{i}+\mathrm{a}_2 \hat{j}+\mathrm{a}_3 \hat{k} \mathrm{a}_i>0, i=1,2,3$ be a vector which makes equal angles with the coordinate axes OX, OY and OZ. Also, let the projection of $\displaystyle \overrightarrow{\mathrm{a}}$ on the vector $\displaystyle 3 \hat{i}+4 \hat{j}$ be $\displaystyle 7$ . Let $\displaystyle \overrightarrow{\mathrm{b}}$ be a vector obtained by rotating $\displaystyle \overrightarrow{\mathrm{a}}$ with $\displaystyle 90^{\circ}$. If $\displaystyle \overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{b}}$ and $\displaystyle x$-axis are coplanar, then projection of a vector $\displaystyle \overrightarrow{\mathrm{b}}$ on $\displaystyle 3 \hat{i}+4 \hat{j}$ is equal to :