Question

in a theater, two spotlights are mounted at different positions. spotlight l1 is at (3, 4, 0) meters. spotlight l2 is at (7, 1, 5) meters. what is the distance between the two spotlights? 6.71 meters 7.07 meters 8.60 meters 9.11 meters

Explanation:

Step1: Recall the distance formula in 3 - D

The distance formula between two points \((x_1,y_1,z_1)\) and \((x_2,y_2,z_2)\) is \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2+(z_2 - z_1)^2}\)
Here, \((x_1,y_1,z_1)=(3,4,0)\) and \((x_2,y_2,z_2)=(7,1,5)\)

Step2: Substitute the values into the formula

\(x_2 - x_1=7 - 3 = 4\), \(y_2 - y_1=1 - 4=-3\), \(z_2 - z_1=5 - 0 = 5\)
\(d=\sqrt{(4)^2+(-3)^2+(5)^2}=\sqrt{16 + 9+25}\)

Step3: Calculate the value

\(d=\sqrt{50}\approx7.07\)

Answer:

7.07 meters