JEE Main · MathematicsEasy

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

Show correct answer & step-by-step solution

Correct answer: A — $x = 1$

Solution

$The equation of a plane passing through point (x_{0}, y_{0}, z_{0}) with normal vector n = ⟨ a, b, c ⟩ is given by a (x - x_{0}) + b (y - y_{0}) + c (z - z_{0}) = 0 .$
$Substitute the given point (1, 1, 1) and the normal vector n = \hat{i} = ⟨ 1, 0, 0 ⟩ into the formula: $1(x - 1) + 0(y - 1) + 0(z - 1) = 0$.$
$Simplify the equation to obtain x - 1 = 0, which results in x = 1 .$
$Hence the answer is (A).$

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