Which of the following is the correct formula for the angle between two planes $A_1 x+B_1 y+C_1 z+D_1$=0 and $A_2 x+B_2 y+C_2 z+D_2$=0?

Question

TuteeHUB · Accepted Answer

NA

TuteeHUB · Answer

cos⁡θ=$\frac{A_1 B_1 C_1}{A_2 B_2 C_2}$

TuteeHUB · Answer

cos⁡θ=$\left |\frac{A_1 A_2+B_1 B_2+C_1 C_2}{\sqrt{A_1^2+B_1^2+C_1^2}\sqrt{A_2^2+B_2^2+C_2^2}}\right |$

TuteeHUB · Answer

sin⁡θ=$\left |\frac{A_1 A_2-B_1 B_2-C_1 C_2}{\sqrt{A_1^2+B_1^2+C_1^2}\sqrt{A_2^2+B_2^2+C_2^2}}\right |$

TuteeHUB · Answer

cos⁡θ=$A_1 A_2+B_1 B_2+C_1 C_2$

1.	Which of the following is the correct formula for the angle between two planes \(A_1 x+B_1 y+C_1 z+D_1\)=0 and \(A_2 x+B_2 y+C_2 z+D_2\)=0?
A.	cos⁡θ=\(\frac{A_1 B_1 C_1}{A_2 B_2 C_2}\)
B.	cos⁡θ=\(\left \|\frac{A_1 A_2+B_1 B_2+C_1 C_2}{\sqrt{A_1^2+B_1^2+C_1^2}\sqrt{A_2^2+B_2^2+C_2^2}}\right \|\)
C.	sin⁡θ=\(\left \|\frac{A_1 A_2-B_1 B_2-C_1 C_2}{\sqrt{A_1^2+B_1^2+C_1^2}\sqrt{A_2^2+B_2^2+C_2^2}}\right \|\)
D.	cos⁡θ=\(A_1 A_2+B_1 B_2+C_1 C_2\)
Answer» C.

Which of the following is the correct formula for the angle between two planes \(A_1 x+B_1 y+C_1 z+D_1\)=0 and \(A_2 x+B_2 y+C_2 z+D_2\)=0?