(i) \(\overline{OP}\)= 4i - 2j + 5k
(ii) Then is perpendicular unit vector to the required plane is
\(\frac{\overline{OP}}{OP}=\frac{4i-2j+5k}{\sqrt{16+4+25}}\\=\frac{4i-2j+5k}{\sqrt{45}}\)
The perpendicular distance from the origin is
\(\sqrt{16+4+25}=\sqrt{45}\)
Vector equation of the Plane can be written as
\(\bar{r}.\bar{m}=d⇒\bar{r}.\frac{4i-2j+5k}{\sqrt{45}}\\=\sqrt{45}{}\)
⇒ \(\bar{r}.4i-2j+5k=45\)
Cartesian from is 4x – 2y + 5z = 45