A vector a- is turned without a change in its length through a small angle d- The value of -a- and a are respectively-

The correct option is B a dθ, 0 From the figure |O⃗A⃗|=a #160;and |O⃗B⃗|=a Also from triangle rule O⃗B⃗ O⃗A⃗=A⃗B⃗=Δa⃗ ⇒ |Δa⃗|=AB us ...

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Byju's Answer

Standard XII

Physics

Vector Addition

A vector a⃗...

Question

A vector $\to a$ is turned without a change in its length through a small angle $d θ$ . The value of $| △ \to a |$ and $△ a$ are respectively:

0, a d θ

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a d θ, 0

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0, 0

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None of these

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Solution

The correct option is B $a d θ, 0$
From the figure $| \to O A | = a$ and $| \to O B | = a$
Also from triangle rule $\to O B - \to O A = \to A B = Δ \to a$
$\Rightarrow | Δ \to a | = A B$
using angle $= \frac{a r c}{r a d i u s}$
$\Rightarrow A B = a . d θ$
So $| Δ \to a | = a d θ$
$Δ a$ means change in magnitude of vector i.e. $| \to O B | - | \to O A |$
$\Rightarrow a - a = 0$
So $Δ a = 0$

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