Let $\overrightarrow{\mathit{d}}$ = $\mathit{x}\hat{\mathit{i}}+\mathit{y}\hat{\mathit{j}}+\mathit{z}\hat{\mathit{k}}$
since $\overrightarrow{\mathit{d}}$ is perpendicular to $\overrightarrow{\mathit{c}}$ and $\overrightarrow{\mathit{b}}$ , so their dot product is zero
$\overrightarrow{\mathit{d}}.\overrightarrow{\mathit{c}}$ = 0 and $\overrightarrow{\mathit{d}}.\overrightarrow{\mathit{b}}$ = 0
3x + y - z = 0 ... (1)
x - 4y + 5z = 0 ... (2)
Also given that $\overrightarrow{\mathit{d}}.\overrightarrow{\mathit{a}}$ = 21.
4x + 5y - z = 21 ... (3)
Solving all the equations simultaneously
x = $-\frac{1}{3}$ , y = $\frac{16}{3}$ , z = $\frac{13}{3}$
$\overrightarrow{\mathit{d}}$ = $\frac{1}{3}$ $\left(-\hat{\mathit{i}}+16\hat{\mathit{j}}+13\hat{\mathit{k}}\right)$