Vectors \underset{A}{\rightarrow},\underset{B}{\rightarrow}\:and\:\underset{C}{\rightarrow} are such that \underset{A}{\rightarrow}.\underset{B}{\rightarrow}=0\:and\:\underset{A}{\rightarrow}.\underset{C}{\rightarrow}=0. Then the vector parallel to \underset{A}{\rightarrow} is

  • Option 1)

    \underset{B}{\rightarrow}\:and\:\underset{C}{\rightarrow}

  • Option 2)

    \underset{A}{\rightarrow}\times \underset{B}{\rightarrow}

  • Option 3)

    \underset{B}{\rightarrow}+ \underset{C}{\rightarrow}

  • Option 4)

    \underset{B}{\rightarrow}\times \underset{C}{\rightarrow}

 

Answers (1)

As learnt in

Vector or cross product -

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

vec A	imes vec B= A, Bsin Theta

- wherein

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

 

shows representation of vector or cross product of vectors

 

 and

Scalar , Dot or Inner Product -

Scalar product of two vector vec{A} & vec{B} written as vec{A} cdot vec{B} is a scalar quantity given by the product of magnitude of vec{A} & vec{B} and the cosine of smaller angle between them.

vec{A}cdot vec{B}= A, Bcdot cos Theta

- wherein

showing representation of scalar products of vectors.

 

 \vec{A}\times \left ( \vec{B} \times \vec{C}\right ) = \vec{B}\left ( \vec{A}\cdot \vec{C} \right ) - \vec{C}\left ( \vec{A} \cdot \vec{B}\right )=0

\Rightarrow \vec{A}\parallel \left ( \vec{B} \times \vec{C}\right )

\mid \because \vec{A}\cdot \vec{B} =0\ and\ \vec{A}\cdot \vec{C} =0

\left ( \vec{A}+\vec{B} \right )^{2}=\left ( \vec{C} \right )^{2}

A^{2}+B^{2}+2\vec{A}\vec{B} = C^{2}

3^{2}+4^{2}+2\vec{A}\cdot \vec{B} = 5^{2}

2\vec{A}\cdot \vec{B}=0\ \ \ \Rightarrow \vec{A}\cdot \vec{B} =0

\vec{A}\perp \vec{B}


Option 1)

\underset{B}{\rightarrow}\:and\:\underset{C}{\rightarrow}

This option is incorrect

Option 2)

\underset{A}{\rightarrow}\times \underset{B}{\rightarrow}

This option is incorrect

Option 3)

\underset{B}{\rightarrow}+ \underset{C}{\rightarrow}

This option is incorrect

Option 4)

\underset{B}{\rightarrow}\times \underset{C}{\rightarrow}

This option is correct

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