Question

Two lines $\overrightarrow{ r }=\overrightarrow{ a }_{1}+\lambda \overrightarrow{ b }_{1}$ and $\overrightarrow{ r }=\overrightarrow{ a }_{2}+\mu \overrightarrow{ b }_{2}$ are said to be coplanar, if

• A. $\left(a_{2}-a_{1}\right) \cdot\left(b_{1} \times b_{2}\right)=0$
• B. $\begin{vmatrix} x _{1} & y _{1} & z _{1} \\ a _{1} & b _{1} & c _{1} \\ a _{2} & b _{2} & c _{2}\end{vmatrix}=0$ where $\left( x _{1}, y _{1}, z _{1}\right)$ are the coordinates of a point on any of the line and $a _{1}, b _{1}, c _{1}$ and $a _{2}, b _{2}, c _{2}$ are the direction ratio of $b _{1}$ and $b _{2}$
• C. Both (a) and (b)
• D. None of the above

Answer 1

Answer: (A)

Correct answer is (a) $\left(a_{2}-a_{1}\right) \cdot\left(b_{1} \times b_{2}\right)=0$