Question

The angle between planes $2x+7y+11z-3=0$ & $5x+3y+9z+1=0$ is .

• A. $co{s}^{-1}\frac{130}{\sqrt{174}.\sqrt{115}}$
• B. $co{s}^{-1}\frac{139}{\sqrt{174}.\sqrt{115}}$
• C. $co{s}^{-1}\frac{123}{\sqrt{174}.\sqrt{115}}$
• D. $co{s}^{-1}\frac{107}{\sqrt{174}.\sqrt{115}}$

Answer 1

The correct option is A $co{s}^{-1}\frac{130}{\sqrt{174}.\sqrt{115}}$

The angle between two planes $a_{1}x+b_{1}y+c_{1}z+d_1=0\&a_{2}x+b_{2}y+c_{2}z+d_2=0$ is given by -$cos\left(\theta \right)=\frac{a_1{a}_2+b_1{b}_2+c_1{c}_2}{\sqrt{(a_1^2+b_1^2+c_1^2)(a_2^2+b_2^2+c_2^2)}}$

$\therefore cos\left(\theta \right)=\frac{2.5+7.3+11.9}{\sqrt{(2^2+7^2+{11}^2)(5^2+3^2+9^2)}}cos\left(\theta \right)=\frac{130}{\sqrt{174}.\sqrt{115}}\left(\theta \right)=co{s}^{-1}\left(\frac{130}{\sqrt{174}\sqrt{115}}\right)$