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16 August, 08:55

A parallelogram is formed by the vectors = (2, 3) and = (1,

1).

a) Determine the lengths of the diagonals.

b) Determine the perimeter of the parallelogram.

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Answers (1)
  1. 16 August, 09:45
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    a) 5 and √5

    b) P = 2 * √13 + 2 * √2

    Step-by-step explanation:

    We add the two vector and for definition the result will be one of the diagonal of the parallelogram. Then

    vector OA (2, 3) vector OB (1. 1)

    If vector OD = OA + OB then

    coordinates of OD will be (2 + 1, 3 + 1) (3, 4)

    And the length of OD is according to Pythagoras Theorem

    |OD| = √ (3) ² + (4) ² = √ 9 + 16 = √25 = 5

    For the other diagonal we need to apply the subtraction of vectors wich will give us the other diagonal

    vector OA = (2, 3) and vector OB = (1, 1)

    If vector BA is the difference between vectors OA - OB then vector BA is

    vector BA = (2 - 1, 3 - 1) = (1, 2)

    And the length of BA is according to Pythagoras Theorem

    BA = √ (1) ² + (2) ² = √1 + 4 = √5

    Then the length of the other diagonal is √ 5

    b) To find the perimeter of the parallelogram we need to apply

    Perimeter = 2 OA + 2 OB

    P = 2 OA + 2 OB (1)

    So length of OA is:

    |OA| = √ (2) ² + (3) ² = √ 13

    and

    |OB| = √ (1) ² + (1) ² = √2

    Then by subtitution in (1)

    P = 2 * √13 + 2 * √2
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