Consider the three displacement vectors = ( 4î − 3ĵ) m, = (3î − 6ĵ) m, and = (−6î + 5ĵ) m. Use the component method to determine the followi

Question

Consider the three displacement vectors = ( 4î − 3ĵ) m, = (3î − 6ĵ) m, and = (−6î + 5ĵ) m. Use the component method to determine the following. (Take the +x direction to be to the right.)

(a) the magnitude and direction of the vector = Darrowbold = A with arrow + B with arrow + C with arrow

magnitude=____ m

direction=____ ° counterclockwise from the +x axis(b) the magnitude and direction of E with arrow = −A with arrow − B with arrow + C with arrow magnitude

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Eirian 4 months 2021-09-05T01:19:38+00:00 1 Answers 16 views 0

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    2021-09-05T01:20:42+00:00

    Answer:

    (a).The magnitude and direction of the vector is 4.12 m and 284°

    (b). The magnitude and direction of the vector is 19.10 m and 313°

    Explanation:

    Given that,

    The  three displacement are

    A=(4i-3j)\ m

    B=(3i-6j)\ m

    C=(-6i+5j)\ m

    We need to calculate the magnitude of the vector

    \vec{D}=\vec{A}+\vec{B}+\vec{C}

    Put the value into the formula

    \vec{D}=(4i-3j)+(3i-6j)+(-6i+5j)

    \vec{D}=(i-4j)

    |\vec{D}|=\sqrt{(1)^2+(4)^2}

    |\vec{D}|=\sqrt{17}

    |\vec{D}|=4.12\ m

    We need to calculate the direction of the vector

    Using formula of direction

    \tan\theta=\dfrac{j}{i}

    \theta=\tan^{-1}(\dfrac{j}{i})

    Put the value into the formula

    \theta=\tan^{-1}(\dfrac{-4}{1})

    \theta=360^{\circ}-76^{\circ}

    \theta=284^{\circ}

    (b). We need to calculate the magnitude of the vector

    \vec{D}=-\vec{A}-\vec{B}+\vec{C}

    Put the value into the formula

    \vec{D}=-(4i-3j)-(3i-6j)+(-6i+5j)

    \vec{D}=(-13i+14j)

    |\vec{D}|=\sqrt{(13)^2+(14)^2}

    |\vec{D}|=19.10\ m

    We need to calculate the direction of the vector

    Using formula of direction

    \tan\theta=\dfrac{j}{i}

    \theta=\tan^{-1}(\dfrac{j}{i})

    Put the value into the formula

    \theta=\tan^{-1}(\dfrac{14}{-13})

    \theta=360^{\circ}-47^{\circ}

    \theta=313^{\circ}

    Hence, (a).The magnitude and direction of the vector is 4.12 m and 284°

    (b). The magnitude and direction of the vector is 19.10 m and 313°

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