Question

Find the unit normal to the plane 4x-2y+z-7=0.

Answer 1

Answer:

$\pm\frac{4\vec{i}-2\vec{j}+1\vec{k}}{\sqrt{21}}$

Step-by-step explanation:

Find the unit normal to the plane 4x-2y+z-7=0.

Concept used:

The unit normal to the plane ax+by+cz+d=0 are

$\pm\frac{a\vec{i}+b\vec{j}+c\vec{k}}{\sqrt{a^2+b^2+c^2}}$

The unit normal to the plane 4x-2y+z-7=0 are

$\pm\frac{4\vec{i}-2\vec{j}+1\vec{k}}{\sqrt{4^2+(-2)^2+1^2}}$

$\pm\frac{4\vec{i}-2\vec{j}+1\vec{k}}{\sqrt{16+4+1}}$

$\pm\frac{4\vec{i}-2\vec{j}+1\vec{k}}{\sqrt{21}}$