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

A
-4/7
B
7/2
C
-7/4
D
2/7

Solution:

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

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

Related content

NEET Rank Assurance Program | NEET Crash Course 2023

JEE Main 2023 Question Papers with Solutions

JEE Main 2024 Syllabus

Best Books for JEE Main 2024

JEE Advanced 2024: Exam date, Syllabus, Eligibility Criteria

JEE Main 2024: Exam dates, Syllabus, Eligibility Criteria

JEE 2024: Exam Date, Syllabus, Eligibility Criteria

NCERT Solutions For Class 6 Maths Data Handling Exercise 9.3

JEE Crash Course – JEE Crash Course 2023

NEET Crash Course – NEET Crash Course 2023