Question

The equation of the plane passing through a point with position vector $\hat{i}+2\hat{j}+3\hat{j}$ and parallel to the plane $\overrightarrow{r}.(3\hat{i}+4\hat{j}+5\hat{j})$

• A. $3x+4y-5_Z+26=0$
• B. $3x+4y+5z-26=0$
• C. $3x-4y+5z-26=0$
• D. $3x+4y-5_Z-26=0$

Answer 1

The correct option is B $3x+4y+5z-26=0$

Since, the plane is parallel to the given plane, The equation of plane is
$3x+4y+5z=d$
The plane passes through the point $(1,2,3)$.
$\therefore 3\left(1\right)+4\left(2\right)+5\left(3\right)=d$
So, the value of $d=26$
Hence, equation of the plane is $3x+4y+5z-26=0$