Question

find the angle between the Planes x+y+z+1=0 and 2x+y+4z+4 =0

Answer 1

♧♧HERE IS YOUR ANSWER♧♧

The planes are :
x + y + z + 1 = 0
2x + y + 4z + 4 = 0

The angle between the two planes being θ be

cosθ
$= \frac{(1.2 + 1.1 + 1.4)}{ \sqrt{ {1}^{2} + {1}^{2} + {1}^{2} } \sqrt{ {2}^{2} + {1}^{2} + {4}^{2} } } \\ \\ = \frac{2 + 1 + 4}{ \sqrt{3} \sqrt{21} } \\ \\ = \frac{7}{ \sqrt{3} \sqrt{3.7} } \\ \\ = \frac{7}{3 \sqrt{7} } \\ \\ = \frac{ \sqrt{7.7} }{3 \sqrt{7} } \\ \\ = \frac{ \sqrt{7} }{3}$

So, the required angle between the lines be θ
$= {cos}^{ - 1} \frac{ \sqrt{7} }{ 3}$

♧♧HOPE THIS HELPS YOU♧♧