Question

The intercept made by the plane $\overrightarrow{r}\cdot \overrightarrow{n}=q$ on the $x$-axis is-

• A. $\frac{q}{\hat{i}\cdot \overrightarrow{n}}$
• B. $\frac{\hat{i}\cdot \overrightarrow{n}}{q}$
• C. $\frac{\hat{i}\cdot \overrightarrow{q}}{n}$
• D. $\frac{q}{\mid \overrightarrow{n}\mid }$

Answer 1

Answer: (A)

$\frac{q}{\hat{i}\cdot \overrightarrow{n}}$

Given plane is, $\overrightarrow{r}\cdot \overrightarrow{n}=q$
When plane intercept $x$-axis, then all the other co-ordinates will be zero. Therefore $\overrightarrow{r}=x\hat{i}$
$\Rightarrow x\hat{i}\cdot \overrightarrow{n}=q$

$\Rightarrow x=\frac{q}{\hat{i}\cdot \overrightarrow{n}}$