Verified by Ajay Kumar
Which of the following lines passes through the origin and forms a 90° angle with the line whose angle of inclination is 30°?
\(y=\tan(30^\circ)\times x\)
\(y=-\tan(30^\circ)\times x\)
\(y=\tan(60^\circ)\times x\)
\(y=-\tan(60^\circ)\times x\)
Answer: D
Solution: The slope of the given line is \(m_1=\tan30^\circ=\frac{1}{\sqrt{3}}\). For two perpendicular lines, \(m_1m_2=-1\). Hence, \(m_2=-\sqrt{3}=-\tan60^\circ\). The required line is \(y=-\tan(60^\circ)\times x\). Trick: The slope of a line perpendicular to a line of slope m is \(-\frac{1}{m}\).
निम्नलिखित में से कौन-सी रेखा मूल बिंदु से गुजरती है और उस रेखा के साथ 90° का कोण बनाती है जिसका झुकाव कोण 30° है?
\(y=\tan(30^\circ)\times x\)
\(y=-\tan(30^\circ)\times x\)
\(y=\tan(60^\circ)\times x\)
\(y=-\tan(60^\circ)\times x\)
उत्तर: D
हल: दी गई रेखा की ढाल \(m_1=\tan30^\circ=\frac{1}{\sqrt{3}}\) है। दो लंबवत रेखाओं के लिए \(m_1m_2=-1\) होता है। इसलिए \(m_2=-\sqrt{3}=-\tan60^\circ\)। आवश्यक रेखा \(y=-\tan(60^\circ)\times x\) है। ट्रिक: m ढाल वाली रेखा पर लंबवत रेखा की ढाल \(-\frac{1}{m}\) होती है।
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