First slide

Scalars and Vectors

Question

A vector $\vec{a}$ is turned without a change in its length through a small angle $d θ$ . The value of $| Δ \vec{a} |$ and $∆ a$ are respectively

Moderate

A

$0, a d θ$
B

$a d θ, 0$
C

$0, 0$
D

None of these

Solution

From the figure $| \vec{O A} | = a and | \vec{O B} | = a$
Also from triangle rule $\vec{O B} - \vec{O A} = \vec{A B} = Δ \vec{a}$
$\begin{array}{l} \Rightarrow | Δ \vec{a} | = A B \\ Using, angle = \frac{arc}{radius} \\ \Rightarrow A B = a \cdot d θ \\ So, | ∆ \vec{a} | = a d θ \end{array}$
$\begin{array}{l} Δ a means change in magnitude of vector, i.e., | \vec{O B} | - | \vec{O A} | \\ \Rightarrow a - a = 0 \\ So Δ a = 0 \end{array}$

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