Final answer:
To find a vector equation with parameter t for the line through the points (-1,-7,-4), we use the concept of a position vector. The equation is r = (-1,-7,-4) + t * (-1,-7,-4)
Step-by-step explanation:
To find a vector equation with parameter t for the line through the points (-1,-7,-4), we can use the concept of a position vector. Let's consider a position vector, r, with coordinates (x,y,z). The vector equation can be represented as r = a + t * b, where a is a position vector to one of the points on the line and b is a direction vector of the line.
Using the given point (-1,-7,-4), the position vector a will be (-1,-7,-4). To find the direction vector b, we can subtract any other point on the line from the given point. Let's say we subtract (0,0,0) from (-1,-7,-4). The direction vector b will be (-1,-7,-4). Therefore, the vector equation will be r = (-1,-7,-4) + t * (-1,-7,-4).