Given P = (3,-4) and Q= (-2, -4) . Sketch PQ. Find the component form, magnitude, and direction of the vector.

Question

Given P = (3,-4) and Q= (-2, -4) . Sketch PQ. Find the component form, magnitude, and direction of the vector.

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Dâu 6 months 2021-07-30T04:56:44+00:00 1 Answers 6 views 0

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    2021-07-30T04:58:33+00:00

    Answer:

    Follows are the solution to this question:

    Step-by-step explanation:

    Given:

    P= (3,-4)\\\\Q=(-2,-4)\\\\\overrightarrow{PQ}=?\\\\Magnitude=?\\\\\text{Direction of the vector}=?\\\\

    Calculating \overrightarrow{PQ}:

    \to \overrightarrow{PQ} = \overrightarrow{Q} -\overrightarrow{P}

              = (-2, -4) - (3,-4)\\\\= (-2\ -3,  -4 \ -(-4)) \\\\= (-5 ,0)\\\\ = -5i+0j

    Calculating magnitude:

    \to || \overrightarrow{PQ} || = \sqrt{i^2+j^2}

                   =\sqrt{-5^2+0^2}\\\\=\sqrt{25+0}\\\\=\sqrt{25}\\\\=5

    Calculating the direction of the vector:

    \overrightarrow{V} = \frac{\overrightarrow{PQ}}{|| \overrightarrow{PQ}||}

       = \frac{5i+0j}{5}\\\\= \frac{5i}{5}\\\\= i

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