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9.Straight Line
medium
ચષ્તુકોણના શિરોબિંદુઓ $(2, -1), (0, 2), (2, 3)$ અને $(4, 0)$ હોય તો તેના વિકર્ણો વચ્ચેનો ખૂણો મેળવો.
A
${90^o}$
B
${0^o}$
C
${\tan ^{ - 1}}(2)$
D
${\tan ^{ - 1}}\left( {\frac{1}{2}} \right)$
(IIT-1986)
Solution
(c)${m_1} = \frac{{3 – ( – 1)}}{{2 – 2}} = \infty ,{m_2} = \frac{{0 – 2}}{{4 – 0}} = \frac{{ – 1}}{2}$
==> $\theta = {\tan ^{ – 1}}\left( {\frac{{ – 1}}{2}} \right) – {90^o}$
$\tan \theta = – \cot \left[ {{{\tan }^{ – 1}}\left( {\frac{{ – 1}}{2}} \right)} \right]\, = – ( – 2) = 2$ ==> $\theta = {\tan ^{ – 1}}(2)$.
Standard 11
Mathematics
