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NCERT · Class 11 · Mathematics · Straight LinesWhat is the angle between two lines whose slopes are $m1 = 2$ and $m2 = 3$?

Q: What is the angle between two lines whose slopes are $m1 = 2$ and $m2 = 3$?

The acute angle $\theta$ between two lines with slopes $m1$ and $m2$ is given by $\tan \theta = \left| \frac{m2 - m1}{1 + m1 m2} \right|$. Substituting $m1 = 2$ and $m2 = 3$: $\tan \theta = \left| \frac{3 - 2}{1 + (2)(3)} \right| = \left| \frac{1}{7} \right| = \frac{1}{7}$. Thus, $\theta = \tan^{-1}(1/7)$. Therefore, the correct option is A.

Step-by-Step Solution

The acute angle $\theta$ between two lines with slopes $m_1$ and $m_2$ is given by $\tan \theta = \left| \frac{m_2 - m_1}{1 + m_1 m_2} \right|$. Substituting $m_1 = 2$ and $m_2 = 3$: $\tan \theta = \left| \frac{3 - 2}{1 + (2)(3)} \right| = \left| \frac{1}{7} \right| = \frac{1}{7}$. Thus, $\theta = \tan^{-1}(1/7)$. Therefore, the correct option is A.

Detailed Options Breakdown

Option : $^\tan-1(1/7)$ (Correct Answer)

Correct choice. Refer to the step-by-step verified solution guidelines above for details.

Option 1: $\tan^{-1}(1/5)$

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Straight Lines.

Option 2: $\tan^{-1}(5)$

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Straight Lines.

Option 3: $\pi/4$

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Straight Lines.

💡 Study Guide: This question tests core syllabus concepts from Straight Lines. For formulas, key summaries, and mock exam reference guides, read the full Straight Lines Revision Notes.

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