Related Questions

    1.

    A unit vector perpendicular to both i^โˆ’2j^+3k^\hat{i} - 2\hat{j} + 3\hat{k} and 2i^+j^โˆ’k^2\hat{i} + \hat{j} - \hat{k} is:

    A

    โˆ’i^+7j^+5k^53\frac{-\hat{i} + 7\hat{j} + 5\hat{k}}{5\sqrt{3}}

    B

    2i^โˆ’j^+3k^14\frac{2\hat{i} - \hat{j} + 3\hat{k}}{\sqrt{14}}

    C

    i^โˆ’2j^โˆ’k^6\frac{\hat{i} - 2\hat{j} - \hat{k}}{\sqrt{6}}

    D

    i^+j^+k^3\frac{\hat{i} + \hat{j} + \hat{k}}{\sqrt{3}}

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    10.

    Given Aโƒ—=4i^+6j^โ€‰andโ€‰Bโƒ—=2i^+3j^{\rm{\vec A}} = 4\hat i + 6\hat j\,and\,{\rm{\vec B}} = 2\hat i + 3\hat j. Which of the following is correct?

    A

    Aโƒ—imesBโƒ—=0โƒ—{\rm{\vec A}} imes {\rm{\vec B}} = \vec 0

    B

    Aโƒ—.Bโƒ—=24{\rm{\vec A}}{\rm{.\vec B}} = 24

    C

    โˆฃAโƒ—โˆฃโˆฃBโƒ—โˆฃ=12\frac{{\left| {{\rm{\vec A}}} \right|}}{{\left| {{\rm{\vec B}}} \right|}} = \frac{1}{2}

    D

    Aโƒ—โ€…โ€Šโ€‰andโ€‰Bโƒ—{\rm{\vec A\;}}\,and\,{\rm{\vec B}} are anti-parallel

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