Question

The acute angle between the diagonals of a parallelogram whose vertices are A(2, -1), B(0, 2), C(2, 3) and D(4,0) is

पर्याय

• \[\cot^{-1}2\]

• \[\cot^{-1}\left(\frac{1}{3}\right)\]

• \[\tan^{-1}2\]

• \[\tan^{-1}\left(\frac{2}{3}\right)\]

Answer 1

\[\tan^{-1}2\]

Explanation:

Here,

Slope of 1^st diagonal (m₁) = \[\frac{3+1}{2-2}=\infty\]

Slope of 2^nd diagonal (m₂) \[={\frac{0-2}{4-0}}=-{\frac{1}{2}}\]

\[\mathrm{tan}\theta=\left|\frac{\mathrm{m}_2-\mathrm{m}_2}{1+\mathrm{m}_1\mathrm{m}_2}\right|\]

\[=\left|\frac{1}{-\frac{1}{2}}\right|\]

\[\therefore\quad\mathrm{tan}\theta=2\]

\[\therefore\quad\theta=\tan^{-1}2\]