Question
Download Solution PDFFind the angle between the pair of lines
\(\frac{{x - 5}}{3} = \frac{{y + 2}}{5} = \frac{{z + 2}}{4}\)
And \(\frac{{x - 1}}{1} = \frac{{y - 3}}{1} = \frac{{z - 3}}{2}\)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCONCEPT:
The angle between the lines with direction ratios \(\left\langle {{a_1},\;{b_1},\;{c_1}} \right\rangle \) and \(\left\langle {{a_2},\;{b_2},\;{c_2}} \right\rangle \) is given by: \(\cos {\bf{\theta }} = \;\frac{{{{\bf{a}}_1}{{\bf{a}}_2} + \;{{\bf{b}}_1}{{\bf{b}}_2} + {{\bf{c}}_1}{{\bf{c}}_2}\;}}{{\sqrt {{\bf{a}}_{1\;}^2 + \;{\bf{b}}_1^2 + \;{\bf{c}}_1^2} \sqrt {{\bf{a}}_{2\;}^2 + \;{\bf{b}}_2^2 + \;{\bf{c}}_2^2} }}\)
Last updated on May 26, 2025
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