Question

Find the equation of the plane that is parallel to the vectors left angle 3 comma 0 comma 3 right angle and left angle 0 comma 1 comma 3 right angle​, passing through the point (2 comma 0 comma negative 1 ).

Answer 1

`x + 3y -z - 3 = 0`

Explanation:

We have to find the equation of plane that is parallel to the vectors

`\langle 3,0,3\rangle, \langle0,1,3\rangle`

The plane also passes through the point (2,0,-1).

Hence, the equation of plane s given by:

`\displaystyle\left[\begin{array}{ccc}x-2&y-0&z+1\\3&0&3\\0&1&3\end{array}\right]\\\\=(x-2)(0-3) - (y-0)(9-0) + (z+1)(3-0)\\=-3(x-2)-9y+3(z+1)\\\Rightarrow -3x + 6 - 9y + 3z + 3 = 0\\\Rightarrow 3x + 9y -3z -9 = 0\\\Rightarrow x + 3y -z - 3 = 0`

It is the required equation of plane.