Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

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 $a_1{a}_2+b_1{b}_2+c_1{c}_2<0$ and origin lies in obtuse angle if $a_1{a}_2+b_1{b}_2+c_1{c}_2>0$. Further point $\left(x_1,y_1,z_1\right)$ and origin both lie either in acute angle or in obtuse angle, if $\left(a_1{x}_1+b_1{y}_1+c_1{z}_1+d_1\right)\left(a_2{x}_1+b_2{y}_1+c_2{z}_1+d_2\right)>0$. One of $\left(x_1,y_1,z_1\right)$ and origin lies in acute angle and the other in obtuse angle, if $\left(a_1{x}_1+b_1{y}_1+c_1{z}_1+d_1\right)\left(a_2{x}_1+b_2{y}_1+c_2{z}_1+d_2\right)<0$. Given the planes $2x+3y-4z+7=0$ and $x-2y+3z-5=0$, if a point P is (1, -2, 3), then