Question 11 Mark

Reduce the equation $\bar{r} \cdot(3 \hat{i}-4 \hat{j}+12 \hat{k})=8$ to the normal form and hence find
(i) the length of the perpendicular from the origin to the plane
(ii) direction cosines of the normal.

Answer

Here $\bar{n}=3 \hat{i}-4 \hat{j}+12 \hat{k} \quad \therefore|\bar{n}|=13$
The required normal form is $\bar{r} \cdot \frac{(3 \hat{i}-4 \hat{j}+12 \hat{k})}{13}=\frac{8}{13}$
(i) the length of the perpendicular from the origin to the plane is $\frac{8}{13}$
(ii) direction cosines of the normal are $\frac{3}{13}, \frac{-4}{13}, \frac{12}{13}$.

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