Let the image of the point (1,0,7) in the line x/1=(y-1)/2=(z-2)/3 be the point (α, β, γ). Then which one of the following points lies on the line passing through (α, β, γ) and making angles (2 π)/3 and (3 π)/4 with y -axis and z -axis respectively and an acute angle with x -axis ?

Three Dimensional Geometry: JEE Main 2024 Mathematics question

JEE Main 2024 · 27 Jan, Evening shift · Q2526

JEE Main 202427 Jan, Evening shiftMathematicsHardThree Dimensional Geometry249× since 2002

Let the image of the point

(1,0,7)

in the line

\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}

be the point

(\alpha, \beta, \gamma)

. Then which one of the following points lies on the line passing through

(\alpha, \beta, \gamma)

and making angles

\frac{2 \pi}{3}

and

\frac{3 \pi}{4}

with

y

-axis and

z

-axis respectively and an acute angle with

x

-axis ?