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23 June, 02:03

El vector a tiene componented ax = 2.70 cm, ay=2.25 cm; y el vector b tiene componentes bx = 0.30 cm, by = 1.75 cm. Calcular las componentes de la resultante a+b

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  1. 23 June, 05:45
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    Given that,

    A vector A has x component to be 2.7cm and y component to be 2.25cm

    Then,

    A = 2.7•i + 2.25•j

    A vector B has x component of 0.30cm and y component of 1.75cm

    B = 0.3•i + 1.75•j

    So, we want to find A+B

    Addition of vectors

    Generally

    (a•i + b•j) + (c•i + d•j) = (a+c) •i + (b+d) •j

    Vectors are added component wise.

    So,

    A + B = (2.7•i + 2.25•j) + (0.3•i + 1.75•j)

    A + B = (2.7 + 0.3) •i + (2.25 + 1.75) •j

    A + B = 3•i + 4•j

    We can also find it magnitude and direction

    Generally,

    A = a•i + b•j

    |A| = √ (a²+b²)


    So,

    |A+B| = √ (3²+4²) = √9+16 = √25

    |A+B| = 5

    And it's direction

    < = arctan (y/x)

    < = arctan (4/3)

    < = 53.13°
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