Let 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 be two planes, where d 1 , d 2 0 . Then origin lies in acute angle if a 1 a 2 + b 1 b 2 + c 1 c 2 1 a 2 + b 1 b 2 + c 1 c 2 …

Question

Let 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 be two planes, where d 1 , d 2 > 0 . Then origin lies in acute angle if a 1 a 2 + b 1 b 2 + c 1 c 2 1 a 2 + b 1 b 2 + c 1 c 2 > 0 . Further point (x 1 , y 1 , z 1 ) and origin both lie either in acute angle or in obtuse angle, if (a 1 x 1 + b 1 y 1 + c 1 z 1 + d 1 ) (a 2 x 1 + b 2 y 1 + c 2 z 1 + d 2 ) > 0 . One of (x 1 , y 1 , z 1 ) and origin lie in acute angle and the other in obtuse angle, if (a 1 x 1 + b 1 y 1 + c 1 z 1 + d 1 ) (a 2 x 1 + b 2 y 1 + c 2 z 1 + d 2 ) Given the planes x + 2y – 3z + 5 = 0 and 2x + y + 3z + 1 =0 . If a point P is (2, –1, 2), then

Accepted Answer

(C) O lies in acute angle, P lies in obtuse angle

Let 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 be two planes…

Answer

Related practice questions