First slide

Vectors

Question

A vector a is turned without a change in its length through a small angles d $θ$ . The value of $|∆ a|$ and $∆$ a are, respectively;

Moderate

A

0, a d $θ$
B

a · d $θ$ ,0
C

0, 0
D

None of these

Solution

$| Δ a | = \sqrt{a^{2} + a^{2} - 2 \cdot a \cdot a \cdot \cos (d θ)} = 2 a \sin (\frac{d θ}{2})$
For small angles $\sin \frac{d θ}{2} \approx \frac{d θ}{2}$
$∴ | Δ a | = 2 a \times \frac{d θ}{2} = \dot{a} \cdot d θ$
$∆$ a means change in magnitude of vector,
i.e., $a - a = 0 \Rightarrow Δ a = 0$

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