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Q.

A vector of length I is turned through the. angle $θ$ about its tail. What is the change in the position vector of its head ?

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a

$2 lcos (θ / 2)$

b

$2 lsin (θ / 2)$

c

$lsin (θ / 2)$

d

$lcos (θ / 2)$

answer is C.

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Detailed Solution

See figure $Δl = l_{2} - l_{1}$

Question Image

where l₂ = l₁ = l
$\begin{array}{l} ∴ Δl = \sqrt{l_{1}^{2} + l_{2}^{2} - 2 l_{1} l_{2} \cos θ} \\ = 2 lsin (θ / 2) \end{array}$

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