Question

A vector \[\vec a\] is turned without a change in its length through a small angle dθ. The value of |Δ\[\vec a\]| and Δa are respectively

Options

• 0, adθ

• adθ, 0

• 0, 0

• adθ, adθ

Answer 1

adθ, 0

Explanation:

From the figure, |\[\overline {OA}\]| = a and |\[\overline {OB}\]| = a

Also from triangle rule, |\[\overline {OB}\]| - |\[\overline {OA}\]| = |\[\overline {AB}\]| = Δ\[\vec a\]

\[\therefore\] |Δ\[\vec a\]| = AB

since dθ = \[\frac {\text {arc}}{\text {radius}}\] ⇒ AB = a dθ

\[\therefore\] |Δ\[\vec a\]| = adθ

Δa means change in magnitude of vector i.e.,

|\[\overline {OB}\]| - |\[\overline {OA}\]|

\[\therefore\] a - a = 0

Hence, Δa = 0