Question

Find the Cartesian form of the equation of a plane whose vector equation is 

 \[\vec{r} \cdot \left( 12 \hat{i} - 3 \hat{j} + 4 \hat{k} \right) + 5 = 0\]

 

Answer 1

` \text{ Substituting }  \vec{r} =\text{ x  }\hat{i} +\text{ y }\hat{j} + \text{ z }\hat{k} \text{ in the given equation, we get } `
\[\left( \text{ x }\hat{i} + \text{ y }\hat{j}  +\text{  z} \hat{k} \right) . \left( \text{ 12 }\hat{i} - \text{ 3 }\hat{j}  + 4 \hat{k} \right) + \text{ 5}= 0\]
\[ \Rightarrow 12x - 3y + 4z + 5 = 0\]