JEE Main · MathematicsEasy

$Find the distance between the points P (1, 2, 3) and Q (3, 4, 5) .$

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Correct answer: B — $23$

Solution

$The distance formula between (x_{1}, y_{1}, z_{1}) and (x_{2}, y_{2}, z_{2}) is (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} + (z_{2} - z_{1})^{2} .$
$Substitute the coordinates: (3 - 1)^{2} + (4 - 2)^{2} + (5 - 3)^{2} .$
$Calculate the squares: 2^{2} + 2^{2} + 2^{2} = 4 + 4 + 4 = 12 .$
$Simplify the radical: 12 = 23 .$
$Hence the answer is (B).$

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