Question

If the line \(\dfrac{x}{-1}=\dfrac{y}{2}=\dfrac{z}{3}\) is parallel to the plane \(ax+by+cz+d=0\) then

• A. \(a+2b+3c=0\)
• B. \(-a+2b+3c=0\)
• C. \(3a+b+2c=0\)
• D. none of these

Hint:

Parallel to plane \(\Rightarrow\) direction vector \(\perp\) plane's normal.

Answer 1

The Correct Option is B

Direction ratios of the line are \((-1,2,3)\). A line parallel to a plane has its direction vector perpendicular to the plane's normal \((a,b,c)\). So their dot product is \(0\): \[ (-1,2,3)\cdot(a,b,c)=-a+2b+3c=0. \]