Final answer:
To find the distance from the point S(7,9,7) to the line x=6t,y=9t, and z=9t, substitute the values into the formula for the distance between a point and a line in three-dimensional space and calculate the distance.
Step-by-step explanation:
To find the distance from the point S(7,9,7) to the line x=6t,y=9t, and z=9t, we can use the formula for the distance between a point and a line in three-dimensional space.
The formula is: d = √((PQ)^2 - ((PQ • V)^2 / V^2))
P is any point on the line, Q is the given point, and V is the direction vector of the line.
In this case, P(6t, 9t, 9t), Q(7, 9, 7), and V(6, 9, 9).
Substituting these values into the formula and simplifying, we get: d = √(520t^2 - 117t + 81)
Since we are asked to find the distance when t = 1, we can substitute t = 1 into the formula and calculate the distance.
d = √(520(1)^2 - 117(1) + 81)
Calculating the distance, we get: d = √(484)
Therefore, the distance from the point S(7,9,7) to the line x=6t,y=9t, and z=9t is approximately 22.