JEE Advance - Mathematics (1983 - No. 2)
A vector $$\overrightarrow A $$ has components $${A_1},{A_2},{A_3}$$ in a right -handed rectangular Cartesian coordinate system $$oxyz.$$ The coordinate system is rotated about the $$x$$-axis through an angle $${\pi \over 2}.$$ Find the components of $$A$$ in the new coordinate system in terms of $${A_1},{A_2},{A_3}.$$
A₁' = A₁, A₂' = A₂, A₃' = A₃
A₁' = A₁, A₂' = -A₃, A₃' = A₂
A₁' = A₁, A₂' = A₃, A₃' = -A₂
A₁' = A₁, A₂' = A₂, A₃' = -A₃
A₁' = A₁, A₂' = -A₂, A₃' = A₃