In the following cases, find the coordinates of the foot of the perpendicular drawn from the origin.(a) `2x + 3y + 4z - 12 = 0` (b) `3y + 4z - 6 = 0`(c) `x + y + z = 1` (d) `5y + 8 = 0`

Explanation

To find the coordinates of the foot of the perpendicular drawn from the origin to the given planes, we will follow these steps for each part of the question.

### Part (a): Plane equation `2x + 3y + 4z - 12 = 0`

1. **Identify the coefficients**: The coefficients of the plane equation are \( A = 2 \), \( B = 3 \), \( C = 4 \), and \( D = -12 \).

2. **Calculate the direction ratios**: The direction ratios of the plane are \( (2, 3, 4) \).

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