1.

    Which of the following is true about opposite vectors?

    A

    They have the same magnitude and direction.

    B

    They have different magnitudes and opposite directions.

    C

    They have the same magnitude but opposite directions.

    D

    They are always position vectors.

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    2.

    Two vectors A⃗ and Bβƒ—{\rm{\vec A}}\,and\,{\rm{\vec B}} are inclined to each other at an angle ΞΈ. Which of the following is the unit vector perpendicular to both A⃗ and Bβƒ—{\rm{\vec A}}\,and\,{\rm{\vec B}} ?

    A

    Aβƒ—imesBβƒ—βˆ£Aβƒ—βˆ£βˆ£Bβƒ—βˆ£\sinheta\frac{\vec{A} imes \vec{B}}{|\vec{A}||\vec{B}|\sinheta}

    B

    Aβƒ—β‹…Bβƒ—βˆ£Aβƒ—βˆ£βˆ£Bβƒ—βˆ£\cosheta\frac{\vec{A} \cdot \vec{B}}{|\vec{A}||\vec{B}|\cosheta}

    C

    Aβƒ—imesBβƒ—βˆ£Aβƒ—βˆ£βˆ£Bβƒ—βˆ£\cosheta\frac{\vec{A} imes \vec{B}}{|\vec{A}||\vec{B}|\cosheta}

    D

    Aβƒ—β‹…Bβƒ—βˆ£Aβƒ—βˆ£βˆ£Bβƒ—βˆ£\sinheta\frac{\vec{A} \cdot \vec{B}}{|\vec{A}||\vec{B}|\sinheta}

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    3.

    Given Aβƒ—=4i^+6j^ and Bβƒ—=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

    A⃗imesB⃗=0⃗{\rm{\vec A}} imes {\rm{\vec B}} = \vec 0

    B

    A⃗.B⃗=24{\rm{\vec A}}{\rm{.\vec B}} = 24

    C

    ∣Aβƒ—βˆ£βˆ£Bβƒ—βˆ£=12\frac{{\left| {{\rm{\vec A}}} \right|}}{{\left| {{\rm{\vec B}}} \right|}} = \frac{1}{2}

    D

    Aβƒ—β€…β€Šβ€‰and Bβƒ—{\rm{\vec A\;}}\,and\,{\rm{\vec B}} are anti-parallel

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    8.

    A→\overrightarrow A is a vector with magnitude A, then the unit vector A^\widehat A in the direction of A→\overrightarrow A is

    A

    AA→A\overrightarrow A

    B

    A→ . Aβ†’\overrightarrow A \,.\,\overrightarrow A

    C

    A→ imes Aβ†’\overrightarrow A \, imes \,\overrightarrow A

    D

    A→A\frac{{\overrightarrow A }}{A}

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