If \hat{n} is a unit vector in the direction of the vector \overrightarrow{A}, then

  • Option 1)

    \hat{n}=\frac{\overrightarrow{A}}{\left | \overrightarrow{A} \right |}

  • Option 2)

    \hat{n}={\overrightarrow{A}}{\left | \overrightarrow{A} \right |}

  • Option 3)

    \hat{n}={\left | \overrightarrow{A} \right |}{\overrightarrow{A}}

  • Option 4)

    None of the above

 

Answers (1)

As learnt in

Important points or Tips for vectors -

1-(Vector Multiplication)

If a vector is multiplied by any scalar (n=1,2,3..) We get again a vector.

\vec{Z}= n\cdot \vec{Y}

Vector Scalar Vector

2-If a vector is multiplied by any real number (eg 2 or -2)  then again, we get a vector quantity.

 

- wherein

If \vec{A} is multiplied by 2 then direction of resultant vector is same as that of given vector.

Vector =2\vec{A}

E.g.

If \vec{A} is multiplied by by (-2), then direction of resultant is opposite to that of given vector.

Vector =-2\vec{A}

 

 If \hat{n} is a unit vector, it's magnitude is equal to \hat{n} = \frac{\vec{A}}{A}

\hat{n} = \frac{\vec{A}}{\left | \vec{A} \right |}


Option 1)

\hat{n}=\frac{\overrightarrow{A}}{\left | \overrightarrow{A} \right |}

This option is correct

Option 2)

\hat{n}={\overrightarrow{A}}{\left | \overrightarrow{A} \right |}

This option is incorrect

Option 3)

\hat{n}={\left | \overrightarrow{A} \right |}{\overrightarrow{A}}

This option is incorrect

Option 4)

None of the above

This option is incorrect

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