If the angle between the lines, x2=y2=z1 and 5−x-2=7y−14P=z−34 is cos−1⁡23, then P is equal to

If the angle between the lines, $\frac{x}{2} = \frac{y}{2} = \frac{z}{1}$ and $\frac{5 - x}{- 2} = \frac{7 y - 14}{P} = \frac{z - 3}{4}$ is $\cos^{- 1} (\frac{2}{3})$ , then $P$ is equal to

$\frac{x}{2} = \frac{y}{2} = \frac{z}{1}, \frac{x - 5}{2} = \frac{y - 2}{\frac{p}{7}} = \frac{z - 3}{4}$

$\cos θ = \frac{2 (2) + 2 (\frac{p}{7}) + 1 (4)}{\sqrt{4 + 4 + 1} \sqrt{4 + (\frac{p^{2}}{49}) + 16}} = \frac{2}{3} \Rightarrow p = \frac{7}{2}$

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