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

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?

TuteeHUB · Accepted Answer

sin u2061 =  (  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 u2061 =  (  frac{A_1 B_1 C_1}{A_2 B_2 C_2}  )

TuteeHUB · Answer

cos u2061 =  (  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 u2061 =  (  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 u2061 =  (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 u2061 = ( frac{A_1 B_1 C_1}{A_2 B_2 C_2} )
B.	cos u2061 = ( 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 u2061 = ( 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 u2061 = (A_1 A_2+B_1 B_2+C_1 C_2 )
Answer» C. sin u2061 = ( 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 \| )

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