If the lines $\frac{x+1}{-10}=\frac{y+\mathrm{k}}{-1}=\frac{z-4}{1}$ and $\frac{x+10}{-1}=\frac{y+1}{-3}=\frac{z-1}{4}$ intersect each other, then the value of $k$ is

Question

Aicharya · Accepted Answer

Since the given lines intersect, $\begin{aligned} & \left|\begin{array}{ccc} x_2-x_1 & y_2-y_1 & z_2-z_1 \ a_1 & b_1 & c_1 \ a_2 & b_2 & c_2 \end{array}ight|=0 \ & \left|\begin{array}{ccc} -10+1 & -1+\mathrm{k} & 1-4 \ -10 & -1 & 1 \ -1 & -3 & 4 \end{array}ight|=0 \ & \Rightarrow\left|\begin{array}{ccc} -9 & -1+\mathrm{k} & -3 \ -10 & -1 & 1 \ -1 & -3 & 4 \end{array}ight|=0 \ & \Rightarrow 39 \mathrm{k}=117 \ & \Rightarrow \mathrm{k}=3 \end{aligned}$

If the lines $\frac{x+1}{-10}=\frac{y+\mathrm{k}}{-1}=\frac{z-4}{1}$ and…

Solution