Find the vector equation of the line passing through the point `(1,2,-4)`and perpendicular to the two lines: `(x-8)/3=(y+19)/(-16)=(z-10)/7`and `(x-15)/3=(y-29)/8=(z-5)/(-5)`

Explanation

To find the vector equation of the line passing through the point \( (1, 2, -4) \) and perpendicular to the two given lines, we will follow these steps:

### Step 1: Identify Direction Ratios of Given Lines
The two lines are given in symmetric form:

1. For the first line:
\[
\frac{x-8}{3} = \frac{y+19}{-16} = \frac{z-10}{7}
...