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A vector vec(a) is turned without a chan...

A vector `vec(a)` is turned without a change in its length through a small angle `d theta`. Find the value of `|Deltavec(a)|` and `Delta a`.

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To solve the problem, we need to analyze the change in the vector \( \vec{A} \) when it is turned through a small angle \( d\theta \) without changing its length. ### Step-by-Step Solution: 1. **Understanding the Initial and Final Vectors**: - Let \( \vec{A} \) be the initial vector with a magnitude \( |\vec{A}| = A \). - After turning the vector through a small angle \( d\theta \), the new vector can be denoted as \( \vec{A}' \). ...
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Knowledge Check

  • The deviation delta of a ray on passing through a prism of small angle A is.

    A
    `(mu - 1)/(A)`
    B
    `(A)/(mu - 1)`
    C
    `(mu - 1) A`
    D
    none of these

  • A vector of length l is turned through the angle theta about its tail. What is the change in the position vector of its head ?

    A
    `l cos (theta//2)`
    B
    `2l sin(theta//2)`
    C
    `2l cos(theta//2)`
    D
    `l sin (theta//2)`

  • A vector of magnitude a is turned through angle theta . The magnitude of change in the vector is given by:

    A
    `|2a sin theta|`
    B
    `|2a sin theta //2|`
    C
    `|(a)/(2) sin theta|`
    D
    `|(a)/(2) sin theta //2|`

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