If a₁, a₂, a₃.....a_n are in H.P., then $\frac{a_{1}}{a_{2} + a_{3} + . . . . . . a_{n}}$ . $\frac{a_{2}}{a_{1} + a_{3} + . . . . . + a_{n}}$ ,...... $\frac{a_{n}}{a_{1} + a_{2} + . . . . . . . + a_{n - 1}}$

are in

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A vector A has components A1,A2,A3 in a right handed rectangular cartesian coordinate system OX,OY,OZ. The coordinate system is rotated about the z-axis through an angle π2 in the anti-clockwise direction. The components of A in the new coordinate system are

The correct option is C A2,−A1,A3When rotated through π2, the new x-axis is along old y-axis and new y-axis is along the old negative x-axis; z-axis remains same as before.Hence, the components of A in the new system are A2,−A1,A3.

A vector $A$ has components $A_{1}, A_{2}, A_{3}$ in a right handed rectangular cartesian coordinate system $O X, O Y, O Z .$ The coordinate system is rotated about the $z$ -axis through an angle $\frac{π}{2}$ in the anti-clockwise direction. The components of $A$ in the new coordinate system are

The correct option is C $A_{2}, - A_{1}, A_{3}$
When rotated through $\frac{π}{2},$ the new x-axis is along old y-axis and new y-axis is along the old negative x-axis; z-axis remains same as before.
Hence, the components of $A$ in the new system are $A_{2}, - A_{1}, A_{3} .$