Question

The straight line $\frac{x-x_0}{\ell }=\frac{y-y_0}{m}=\frac{z-z_0}{n}$ is parallel to the plane $ax+by+cz=d$ then:

• A. $\frac{a}{\ell }=\frac{b}{m}=\frac{c}{n}$
• B. $a\ell =bm=cn$
• C. $\frac{a}{\ell }+\frac{b}{m}+\frac{c}{n}$
• D. $a\ell +bm+cn=0$

Answer 1

Answer: (D)

The direction ratios of given line are $\ell ,m,n$ and that of the normal of the given plane are $a,b,c$. Since the line and the plane are mutually parallel, therefore the line and normal to the plane must be mutually perpendicular. Hence, according to the condition of perpendicularity, we obtain $a\ell +bm+cn=0$