JEE Main · MathematicsEasy

$Find the distance between the points P (1, 2, 3) and Q (4, 6, 3) .$

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Correct answer: C — $5$

Solution

$Identify the coordinates of the points as P (x_{1}, y_{1}, z_{1}) = (1, 2, 3) and Q (x_{2}, y_{2}, z_{2}) = (4, 6, 3) .$
$Apply the 3D distance formula: d = (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2} + (z_{2} - z_{1})^{2} .$
$Substitute the coordinates into the formula: d = (4 - 1)^{2} + (6 - 2)^{2} + (3 - 3)^{2} .$
$Simplify the expression: d = 3^{2} + 4^{2} + 0^{2} = 9 + 16 = 25 = 5 .$
$Hence the answer is (C).$

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