Question

Find the angle between planes 2x +7y +11z - 3 = 0 & 5x +3y +9z +1 = 0

• 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 $co{s}^{-1}=\frac{130}{\sqrt{174}.\sqrt{115}}$

We know that 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 -
$cos\left(\theta \right)=\frac{a_1{a}_2+b_1{b}_2+c_1{c}_2}{\sqrt{(a_1^2+b_1^2+c_1^2)(a_2^2+b_2^2+c_2^2)}}$
So, Here we’ll substitute the appropriate values.
$cos\left(\theta \right)=\frac{2.5+7.3+11.9}{\sqrt{(2^2+7^2+{11}^2)(5^2+3^2+9^2)}}$
$cos\left(\theta \right)=\frac{130}{\sqrt{174}.\sqrt{115}}$
$\left(\theta \right)=co{s}^{-1}\left(\frac{127}{\sqrt{174}\sqrt{115}}\right)$