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10 September, 03:31

Find the component form of the vector v ⃗ with ‖v ⃗ ‖=4√3 when drawn in standard position v ⃗ lies in Quadrant II and makes a 30° angle with the positive y-axis. Give exact values.

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  1. 10 September, 03:37
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    The answer:

    first of all, we should know that the expression of a vector V (a, b) can be written as follow:

    V = r (Vx i + Vyj), where r is the length of the vector, it is r = sqrt (V²x + V²y)

    Vx is the component lying on the x-axis and Vy on the y-axis

    v ⃗ lies in Quadrant II, means Vx is less than 0 (negative)

    so Vx = - r sin30° and Vy = rcos30°

    r = ‖v ⃗ ‖=4√3

    so we have v = - 4√3sin30° i + 4√3 cos30° j

    the components are

    v ( - 4√3sin30°, 4√3 cos30°) = (-2√3, 4√3 cos30°)
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