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10.8E: Vectors (Mazoezi)

  • Page ID
    178529
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    Kwa mazoezi yafuatayo, onyesha kama vectors mbili,\(\mathbf{u}\) na\(\mathbf{v},\) ni sawa, ambapo\(\mathbf{u}\) ina hatua ya awali\(P_{1}\) na hatua ya mwisho\(P_{2},\) na\(\mathbf{v}\) ina hatua ya awali\(P_{3}\) na hatua ya mwisho\(P_{4}\).

    52. \(P_{1}=(-1,4), P_{2}=(3,1), P_{3}=(5,5)\)na\(P_{4}=(9,2)\)

    53. \(P_{1}=(6,11), P_{2}=(-2,8), P_{3}=(0,-1)\)na\(P_{4}=(-8,2)\)

    Kwa mazoezi yafuatayo, tumia vectors\(\mathbf{u}=2 \mathbf{i}-\mathbf{j}, \mathbf{v}=4 \mathbf{i}-3 \mathbf{j},\) na\(w=-2 \mathbf{i}+5 \mathbf{j}\) kutathmini maneno.

    54. \(u-v\)

    55. \(2 v-u+w\)

    Kwa mazoezi yafuatayo, pata vector kitengo katika mwelekeo sawa na vector iliyotolewa.

    56. \(a=8 i-6 j\)

    57. \(b=-3 i-j\)

    Kwa mazoezi yafuatayo, pata ukubwa na mwelekeo wa vector.

    58. \(\langle 6,-2\rangle\)

    59. \(\langle-3,-3\rangle\)

    Kwa mazoezi yafuatayo, hesabu\(\mathbf{u} \cdot \mathbf{v}\).

    60. \(u=-2 i+j\)na\(v=3 i+7 j\)

    61. \(u=i+4 j\)na\(v=4 i+3 j\)

    62. Kutokana na\(\boldsymbol{v}=\langle-3,4\rangle\) kuteka\(\boldsymbol{v}, 2 \boldsymbol{v},\) na\(\frac{1}{2} \boldsymbol{v}\)

    63. Kutokana na wadudu inavyoonekana katika Kielelezo 4, mchoro\(\boldsymbol{u}+\boldsymbol{v}, \boldsymbol{u}-\boldsymbol{v}\) na\(3 \boldsymbol{v}\).

    Mchoro wa vectors v, 2v, na 1/2 v. vector 2v iko katika mwelekeo sawa na v lakini ina ukubwa mara mbili. the 1/2 v vector ni katika mwelekeo sawa na v lakini ina nusu ukubwa.

    Kielelezo 4

    64. Kutokana\(P_{1}=(3,2)\) na hatua ya awali na hatua ya mwisho\(P_{2}=(-5,-1),\) kuandika vector\(\mathbf{v}\) katika suala la\(\mathbf{i}\) na\(\mathbf{j}\). Chora pointi na vector kwenye grafu.