Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

If a line $\frac{x-x_1}{a_1}=\frac{y-y_1}{b_1}=\frac{z-z_1}{c_1}$ lies on a plane $a_{2}x+b_{2}y+c_{2}z=d,$ then (i) $a_1{a}_2+b_1{b}_2+c_1{c}_2=0$ (ii) $a_2{x}_1+b_2{y}_1+c_2{z}_1=d$ According to the question. $3(1)+(2+\lambda )(-2)+(-1)(0)=0$ $\Rightarrow 3-4-2\lambda =0$ $\Rightarrow \lambda =-1/2$ Also, $\lambda -2=0$ $\Rightarrow \lambda =2$ So. there is no such value of $\lambda$