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Definition of Vector

A vector a⃗...

Question

A vector $\to a$ has components $a_{1}, a_{2}, a_{3}$ in a right handed rectangular cartesian coordinates system $O X Y Z$ . The coordinate system rotated about $y$ -axis through an angle $\frac{π}{2}$ The components of $\to a$ in the new system are

A

(- a_{1}, a_{2}, a_{3})

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B

(a_{2}, a_{1}, a_{3})

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C

(- a_{3}, a_{2}, a_{1})

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D

(a_{3}, a_{2}, a_{1})

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Solution

The correct option is C $(- a_{3}, a_{2}, a_{1})$
Given $\to a = (a_{1}, a_{2}, a_{3})$
Since the coordinate system OXYZ is rotated about y-axis through an angle of $\frac{π}{2}$ , so y component will remain same and new z-axis is along OX,and new x-axis is along OZ'
So, the new component of $\to a$ are $(- a_{3}, a_{2}, a_{1})$

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Similar questions

A

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

a_{1}, a_{2}, a_{3}, . . . 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_{3}}{a_{1} + a_{2} + a_{4} + . . . + a_{n}}, \frac{a_{n}}{a_{1} + a_{2} + . . . + a_{n}}

a_{1}, a_{2}, a_{3}, . . . . 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}}

a_{1}, a_{2}, a_{3}, . . . . . 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}}

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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