JEE Advanced · MathematicsEasy

$What is the equation of the plane passing through the point (1, 1, 1) and perpendicular to the vector n = \hat{i} + \hat{j} + \hat{k} ?$

Show correct answer & step-by-step solution

Correct answer: C — $x + y + z = 3$

Solution

$The normal vector is n = (1, 1, 1) and the point is (x_{0}, y_{0}, z_{0}) = (1, 1, 1) .$
$The equation of the plane is a (x - x_{0}) + b (y - y_{0}) + c (z - z_{0}) = 0 .$
$Substitute the values: $1(x-1) + 1(y-1) + 1(z-1) = 0$.$
$Simplify the expression: x - 1 + y - 1 + z - 1 = 0, which gives x + y + z = 3 .$
$Hence the answer is (C).$

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