​ Find the Cartesian equation of the plane whose vector equation isr (3i + 5j - 9k) = 8.

Question

Find the Cartesian equation of the plane whose vector equation is \(\bar{r}\)(3\(\hat{i}\) + 5\(\hat{j}\) - 9\(\hat{k}\)) = 8

Answer 1

Given : 

Vector equation of the plane is

 \(\bar{r}\).(3\(\hat{i}\) + 5\(\hat{j}\) - 9\(\hat{k}\)) = 8

To Find : Cartesian equation of the given plane. 

Formulae : 

1) Dot Product : 

If \(\bar{a}\) & \(\bar{b}\) are two vectors

= (x × 3) + (y × 5) + (z × (-9)) 

= 3x + 5y – 9z 

Therefore equation of the plane is 

3x + 5y – 9z = 8 

This is the Cartesian equation of the given plane.