Find the distance between the point A (1, 2, 5) and B (3, - 5, 0) ?

  1. \( \sqrt {67}\)
  2. \( \sqrt {71}\)
  3. \( \sqrt {78}\)
  4. None of these

Answer (Detailed Solution Below)

Option 3 : \( \sqrt {78}\)
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Detailed Solution

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CONCEPT:

If A(x1, y1, z1) and B(x2, y2, z2) then the distance between the points A and B is given by: \(\sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2} + {{\left( {{z_2} - {z_1}} \right)}^2}} \)

CALCULATION:

Given: A (1, 2, 5) and B (3, - 5, 0) are two points in a 3D space.

Here, we have to find the distance between the the given points.

As we know that, if A(x1, y1, z1) and B(x2, y2, z2) then the distance between the points A and B is given by: \(\sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2} + {{\left( {{z_2} - {z_1}} \right)}^2}} \)

⇒ \(d = \sqrt {{{\left( {{3} - {1}} \right)}^2} + {{\left( {{-5} - {2}} \right)}^2} + {{\left( {{0} - {5}} \right)}^2}} = \sqrt {78} \ units\) 
 
Hence, option C is the correct answer.
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