If \overrightarrow{P}\times{\overrightarrow{Q}}=\overrightarrow{R} then which of the following statement is not true?

 

  • Option 1)

    \overrightarrow{R}\perp \overrightarrow{P}

  • Option 2)

    \overrightarrow{R}\perp \overrightarrow{Q}

  • Option 3)

    \overrightarrow{R}\perp \left ( \overrightarrow{P}+ \overrightarrow{Q} \right )

  • Option 4)

    \overrightarrow{R}\perp \left ( \overrightarrow{P}\times \overrightarrow{Q} \right )

 

Answers (1)

As we discussed in

Vector or cross product -

Vector or cross product of two vector \vec{A} & \vec{B} written asA\times B is a single vector whose magnitude is equal to product of magnitude of \vec{A} & \vec{B} and the sine of smaller angle\Theta  between them.

\vec A\times \vec B= A\, B\sin \Theta

- wherein

Figure 6 shows representation of vector or cross product of vectors.

 

shows representation of vector or cross product of vectors

 

 Form the property of vector product, we notice that \vec{R} must be perpendicular to the plane formed by vector \vec{P} and \vec{Q}. Thus \vec{R} is Perpendicular to both \vec{P} and \vec{Q} and (\vec{P}+\vec{Q}) Vector also.


Option 1)

\overrightarrow{R}\perp \overrightarrow{P}

Option is Incorrect

Option 2)

\overrightarrow{R}\perp \overrightarrow{Q}

Option is Incorrect

Option 3)

\overrightarrow{R}\perp \left ( \overrightarrow{P}+ \overrightarrow{Q} \right )

Option is Incorrect

Option 4)

\overrightarrow{R}\perp \left ( \overrightarrow{P}\times \overrightarrow{Q} \right )

Option is Correct

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