Find the angle between the lines y = (2 – 3)(x + 5) and y = (2 + 3)(x – 7).

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Vishal Baghel | Contributor-Level 10

a year ago

This is a Short Answer Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l} T h e g i v e n e q u a t i o n s a r e y = (2 - \sqrt[]{3}) (x + 5) \dots (i) \\ a n d y = (2 + \sqrt[]{3}) (x - 7) \dots (i i) \\ S l o p e o f t h e e q n . (i) m_{1} (s a y) = (2 - \sqrt[]{3}) \\ a n d s l o p e o f t h e e q n . (i i) m_{2} (s a y) = (2 + \sqrt[]{3}) \\ L e t θ b e t h e a n g l e b e t q w e e n t h e t w o g i v e n l i n e s \\ ∴ t a n θ = | \frac{m_{1} - m_{2}}{1 + m_{1} m_{2}} | = | \frac{2 - \sqrt[]{3} - 2 - \sqrt[]{3}}{1 + (2 - \sqrt[]{3}) (2 + \sqrt[]{3})} | = | \frac{- 2 \sqrt[]{3}}{2} | = | - \sqrt[]{3} | \\ \Rightarrow t a n θ = \sqrt[]{3} o r - \sqrt[]{3} \\ ∴ θ = 6 0^{0} o r 12 0^{0} \\ H e n c e, t h e r e q u i r e d a n g l e i s 6 0^{0} o r 12 0^{0} . \end{array}$

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