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Integration of Piecewise Continuous Functions

With respect ...

Question

With respect to rectangular coordinate system $O X Y Z$ , $\to a$ has components $(2, 4, 8)$ . The system is rotated through an angle of $\frac{π}{2}$ about X-axis. The components of $\to a$ in the new system are

A

(2, 8, 4)

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B

(2, 8, - 4)

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C

(2, - 8, 4)

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D

(2, - 8, - 4)

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Solution

The correct option is A $(2, - 8, 4)$
$\to a = (2, 4, 8)$
Compnents of $\to a$ are ${\to a}_{1}, {\to a}_{2}, {\to a}_{3}$ along coordinates axes
$a_{1} = 2, a_{2} = 4, a_{3} = 8$ , $a_{2} = a cos α, a_{3} = a sin α$
let new components of $\to a$ be $A_{1}, A_{2}, A_{3}$
$A_{1}$ remains the same as system is rotated along X axis.
$A_{2} = a cos (α + \frac{π}{2}) = - a sin α = - a_{3} = - 8$
$A_{3} = a sin (α + \frac{π}{2}) = a cos α = a_{2} = 4$

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