Question:
the perpendicular distance from the origin to the plane containing the two lines,
$\frac{x+2}{3}=\frac{y-2}{5}=\frac{z+5}{7}$ and $\frac{x-1}{1}=\frac{y-4}{4}=\frac{z+4}{7}$ is
Correct Option: 1
Solution:
$\left|\begin{array}{lll}\mathrm{i} & \mathrm{j} & \mathrm{k} \\ 3 & 5 & 7 \\ 1 & 4 & 7\end{array}\right|$
$\hat{\mathrm{i}}(35-28)-\hat{\mathrm{j}}(21.7)+\hat{\mathrm{k}}(12-5)$
$7 \hat{\mathrm{i}}-14 \hat{\mathrm{j}}+7 \hat{\mathrm{k}}$
$\hat{i}-2 \hat{j}+\hat{k}$
$1(x+2)-2(y-2)+1(z+15)=0$
$x-2 y+z+11=0$
$\frac{11}{\sqrt{4+1+1}}=\frac{11}{\sqrt{6}}$
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