Distance between the points A(log10 1000, tan 45°), B(cosec 30°,log 343) is

Question

Distance between the points A(log₁₀ 1000, tan 45°), B(cosec 30°,log₇ 343) is 

A) \(\sqrt{13T}\) units 

B) \(\sqrt{10}\) units 

C) \(\sqrt{34}\) units

D) √5 units

Answer 1

Correct option is (D) √5 units

Given points are \(A\,(log_{10}\,1000,tan\,45^\circ)\)

\(=(log_{10}\,10^3,1)\) \(=(3,1)\)

And \(B\,(cosec\,30^\circ,log_7\,343)\)

\(=(2,log_7\,7^3)=(2,3)\)

i.e., \(A(3,1)\;\&\;B(2,3)\)

\(\therefore\) Distance between points A & B is

\(AB=\sqrt{(2-3)^2+(3-1)^2}\)

\(=\sqrt{(-1)^2+2^2}\)

\(=\sqrt{1+4}\) \(=\sqrt{5}\) units

Answer 2

Correct option is D) √5 units