two vectors undergo vector addition. vector a has a magnitude of 217 units and points to the north. vector b has a magnitude of 156 units an

two vectors undergo vector addition. vector a has a magnitude of 217 units and points to the north. vector b has a magnitude of 156 units and points to the west. what is the direction of the resultant vector? (the angle)

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  1. Explanation:

    Given that,

    The magnitude of vector A = 217 units to north

    The magnitude of vector B = 156 units to west

    Let R is the resultant. So,

    [tex]R=\sqrt{217^2+156^2} \\\\R=267.25\ \text{units}[/tex]

    Let [tex]\theta[/tex] is the direction of the resultant vector. So,

    [tex]\tan\theta=\dfrac{y}{x}\\\\\tan\theta=\dfrac{217}{156}\\\\\theta=\tan^{-1}\left(\dfrac{217}{156}\right)\\\\\theta=54.28^{\circ}[/tex]

    Hence, this is the required solution.

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