Three Dimensional Geometry: JEE Main 2023 Mathematics question

JEE Main 2023 · 30 Jan, Evening shift · Q2457

JEE Main 202330 Jan, Evening shiftMathematicsMediumThree Dimensional Geometry249× since 2002

A vector

\vec{v}

in the first octant is inclined to the

x

-axis at

60^{\circ}

, to the

y

-axis at 45 and to the

z

-axis at an acute angle. If a plane passing through the points

(\sqrt{2},-1,1)

and

(a, b, c)

, is normal to

\vec{v}

, then :