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Let a1x+b1y+c1z+d1=0 and a2x+b2y+c2z+d2=...

Let `a_1x+b_1y+c_1z+d_1=0 and a_2x+b_2y+c_2z+d_2=0 ` be two planes, where `d_1, d_2gt0`. Then, origin lies in acute angle, If `a_1a_2+b_1b_2+c_1c_2lt0` and origin lies in obtuse angle if `a_1a_2+b_1b_2+c_1c_2gt0`.
Further point `(x_1, y_1, z_1)` and origin both lie either in acute angle or in obtuse angle. If ( `a_1x_1+b_1y_1+c_1z_1+d_1)(a_2x_1+b_2y_1+c_2z_1+d_2)gt0`.
one of `(x_1, y_1, z_1)` and origin in lie in acute and the other in obtuse angle,If ( `a_1x_1+b_1y_1+c_1z_1+d_1)(a_2x_1+b_2y_1+c_2z_1+d_2)lt0`
Q. Given that planes `2x+3y-4z+7=0 and x-2y+3z-5=0`. If a point `P(1, -2, 3),` then
a. O and P both lie in acute angle between the planes
b.O and P both lies in obtuse angle
c.O lies in acute angle, P lies in obtuse angle
d. O lies in obtuse angle, P lies in acute angle

A

O and P both lie in acute angle between the planes

B

O and P both lies in obtuse angle

C

O lies in acute angle, P lies in obtuse angle

D

O lies in obtuse angle, P lies in acute angle

Text Solution

Verified by Experts

The correct Answer is:
A
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