Question

Find the line through the point a parallel to the line of intersection of the planes $r\cdot n_1=1,r\cdot n_2=1$

• A. $r=a+t(n_1\times n_2)$
• B. $r=a+t(a\times n_2)$
• C. $r=n_1+t(a\times n_2)$
• D. $r=n_2+t(a\times n_1)$

Answer 1

Answer: (A)

$r=a+t(n_1\times n_2)$

The direction vector of the line of the intersection of the following planes will be

$=(\overrightarrow{n_1}\times \overrightarrow{n_2})$.

Now it is given that the line passes through the point which is denoted by the vector $\overrightarrow{a}$.

Hence the equation of the line will be

$\overrightarrow{r}=\overrightarrow{a}+\mu (\overrightarrow{n_1}\times \overrightarrow{n_2})$