A vector v in the first octant is inclined to the x-axis at 60^°,… | JEE Main 2023 Mathematics PYQ

MCQMediumJEE Main 2023 · 30 January, Shift 2Equation of Plane

A vector $\mathbf{v}$ in the first octant is inclined to the x-axis at $60^\circ$ , to the y-axis at $45^\circ$ and to the z-axis at an acute angle. If a plane passing through the points $\left( \sqrt{2}, -1, 1 \right)$ and $(a, b, c)$ , is normal to $\mathbf{v}$ , then

A
$\sqrt{2}a + b + c = 1$
B
$a + b + \sqrt{2}c = 1$
C
$a + \sqrt{2}b + c = 1$
D
$\sqrt{2}a - b + c = 1$

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