The Cartesian equation of the plane `vecr=(1+lamda-mu)hati+(2-lamda)hatj+(3-2lamda+2mu)hatk` is a. `2x+y=5` b.`2x-y=5` c.`2x+z=5` d.`2x-z=5`

Options

A. `2x+y=5`
B. `2x-y=5`
C. `2x+z=5`
D. `2x-z=5`

Explanation

To find the Cartesian equation of the plane given by the vector equation \(\vec{r} = (1 + \lambda - \mu) \hat{i} + (2 - \lambda) \hat{j} + (3 - 2\lambda + 2\mu) \hat{k}\), we will follow these steps:

### Step 1: Identify the components of the vector equation
The vector equation can be broken down into its components:
- \(x = 1 + \lambda - \mu\)
- \(y = 2 - \lambda\)
- \(z = 3 - 2\lambda + 2\mu\)