Solution
We are given the cylindrical coordinates. we have to convert these to regular coordinates of the cartesian plane as shown below;
First point;
to find "x" , we apply "x= r \u00d7 cos(\\theta)"
"= 10.32\u00d7 cos(-0.32)"
"=9.7961"
to find "y" , we apply "y = r\u00d7 sin(\\theta)" `
"= 10.32\u00d7 sin(-0.32)"
"= -3.2463"
And "z" remains the same i.e. "z= 45.3"
Now the first point "p_1 = (9.7961, -32463, 45.3)"
Second point;
Finding "x" ; "x= r \u00d7 cos(\\theta)"
"= 10.33\u00d7 cos (-0.31)"
"= 9.8376"
`
Finding "y" ; "y = r\u00d7 sin(\\theta)"
"= 10.33 \u00d7 sin (-0.31)"
"=-3.1513"
And "z" remains the same i.e. "z= 45.27"
The second point, "p_2 = (9.8376, -3.1513, 45.27)"
Now having the position of the two objects, we find the distance between them; which is given by;
"D^2 = X^2 + Y^2 + Z^2"
To find the "X, Y, and, Z" , we Calculate the positive difference between each coordinates, i.e
"X= 9.8376-9.7961"
"=0.0415"
"Y = -3.1513 - -3.2463"
"=0.095"
"Z = 45.3-45.27"
"=0.03"
Now having the values, we calculate;
"D^2 = X^2 + Y^2 + Z^2"
"= 0.0415^2 + 0.095^2 +0.03^2"
"= 0.00172225 + 0.009025 +0.0009"
"= 0.01164725"
"D = \\sqrt{ 0.01164725}"
"= 0.1079"
Therefore the distance between the two objects is "0.1079" "Units"
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