Question

If $4x+4y-kz=0$ is the equation of the plane through the origin that contains the line $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z}{4},$ then $k=$

• A. $1$
• B. $3$
• C. $5$
• D. $7$

Answer 1

The correct option is C $5$

Equation of the plane is $4x+4y-kz=0$ …………$\left(1\right)$

the plane $\left(1\right)$ contains the line $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z}{4}$

$\therefore$ The given plane $\left(1\right)$ must be parallel to $2,3,4$, which are the direction ratios of the line.

$\Rightarrow 4\left(2\right)+4\left(3\right)+(-k)4=0$

$\Rightarrow 8+12-4k=0$

$\Rightarrow 4k=20$

$\Rightarrow k=5$.