Question

Two tanks are participating in a battle simulation. Tank A is at point

(345, 870, 565) and tank B is positioned at point (785, 635, 597).

1.Find parametric equations for the line of sight between the tanks. (Use the parameter t.)

(x(t), y(t), z(t)) = _________ for 0 ≤ t ≤ 1

2. If we divide the line of sight into 5 equal segments, the elevations of the terrain at the four intermediate points from tank A to tank B are 549, 568, 587, and 588. Can the tanks see each other?(choose one)

A. The tanks can see each other.
B. The tanks can't see each other.

Answer 1

The parametric equations for the line of sight between the tanks are x(t) = 345 + (785 - 345)t, y(t) = 870 + (635 - 870)t, and z(t) = 565 + (597 - 565)t. The tanks can't see each other because the elevation of the line of sight at the intermediate points is higher than the terrain elevations.

Step-by-step explanation:

The parametric equations for the line of sight between the tanks are:

x(t) = 345 + (785 - 345)t

y(t) = 870 + (635 - 870)t

z(t) = 565 + (597 - 565)t

where 0 ≤ t ≤ 12.

To determine if the tanks can see each other, we need to compare the elevations of the terrain with the elevation of the line of sight at the intermediate points. If the line of sight is higher than the terrain at any of the points, the tanks can't see each other. In this case, the elevation of the line of sight at the intermediate points is 568, which is higher than all the terrain elevations. Therefore, the tanks can't see each other.