The vector $\overrightarrow P = a\hat i + a\hat j + 3\hat k$ and $\overrightarrow Q = a\hat i - 2\hat j - \hat k$ are perpendicular to each other. The positive value of $a$ is

  • [AIIMS 2002]
  • A

    $3$

  • B

    $4$

  • C

    $9$

  • D

    $13$

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$\vec A$ and $\vec B$ are two vectors and $\theta$ is the angle between them, if $|\vec A \times \vec B|=\sqrt 3(\vec A \cdot \vec B) $ the value of $\theta$ is ......... $^o$

  • [AIPMT 2007]

Show that the scalar product of two vectors obeys the law of distributive.

If $F _1$ and $F _2$ are two vectors of equal magnitudes $F$ such that $\left| F _1 \cdot F _2\right|=\left| F _1 \times F _2\right|$, then $\left| F _1+ F _2\right|$ equals to

If for two vectors $\overrightarrow A $ and $\overrightarrow B ,\overrightarrow A \times \overrightarrow B = 0,$ the vectors

Obtain scalar product in terms of Cartesian component of vectors.