The vector v has initial point P(1, 0) and terminal point Q that is on the y-axis and above the initial point. Find the coordinates of termi

Question

The vector v has initial point P(1, 0) and terminal point Q that is on the y-axis and above the initial point. Find the coordinates of terminal point Q such that the magnitude of the vector v is 65 .

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Adalyn 3 weeks 2021-11-21T11:15:36+00:00 1 Answer 0 views 0

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    2021-11-21T11:16:59+00:00

    Answer:

    The terminal point is Q(0,4)

    Step-by-step explanation:

    We are given the following in the question:

    Initial point of vector, P(1,0)

    The terminal point Q lies on the y-axis, thus Q have coordinates of the form:

    Q(0,y)

    The magnitude of the vector is \sqrt{65}

    Magnitude is given by:

    v = \sqrt{(x_2-x_2)^2+(y_2-y_1)^2}\\\sqrt{65}=\sqrt{(0-1)^2+(y-0)^2}\\\sqrt{65}=\sqrt{1+y^2}\\65 = 1+y^2\\y^2 = 64\\y = \pm 8

    But since the terminal point is above the initial point, thus,

    y > 0\\\Rightarrow y = 4

    Thus, the terminal point is Q(0,4)

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