Question

If the lines $\overline{r}=\overline{a}+\lambda (\overline{b}\times \overline{c})$ and $\overline{r}=\overline{b}+\mu (\overline{c}\times \overline{a})$ intersect each other then the condition is

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

$\Rightarrow$ $(\overline{a}-\overline{b})\cdot (\overline{b}\times \overline{c})\times (\overline{c}\times \overline{a})$ =0

$\Rightarrow$ $(\overline{a}-\overline{b})\cdot \left[\overline{b}\overline{c}\overline{a}\right]\overline{c}$ =0

$\Rightarrow$ $(\overline{a}-\overline{b})\cdot \overline{c}$ =0

$\Rightarrow$ $\overline{a}\cdot \overline{c}=\overline{b}\cdot \overline{c}$