Answer

Verified

477.9k+ views

Hint: Here, we will use the formulae of unit vector in the direction of unit vector to solve.

Given,

Vector is$\widehat i + \widehat j + \widehat k$. Now, we need to find the unit vector in the direction of $\widehat i + \widehat j + \widehat k$. As, we know that a unit vector is given by dividing the vector by its magnitude, so the resulting vector has magnitude 1and is in same direction as the original vector.

Let$\widehat a = \widehat i + \widehat j + \widehat k$, Now magnitude of $\widehat a$is

\[\begin{gathered}

\Rightarrow \left| {\widehat a} \right| = \sqrt {{1^2} + {1^2} + {1^2}} \\

\Rightarrow \left| {\widehat a} \right| = \sqrt 3 \\

\end{gathered} \]

As, we know the unit vector in the direction of $\widehat a $ is $\dfrac{{\widehat a}}{{\left| {\widehat a} \right|}}$.Now, the unit vector in the direction of $\widehat i + \widehat j + \widehat k$ will be

$ \Rightarrow \dfrac{{\widehat i + \widehat j + \widehat k}}{{\sqrt 3 }}$

Therefore, the unit vector in the direction of $\widehat i + \widehat j + \widehat k$ is $\dfrac{{\widehat i + \widehat j + \widehat k}}{{\sqrt 3 }}$.

Hence, the required option for the given question is ‘A’.

Note: Here, we have been asked to find the unit vector in the direction of the vector, hence the sign of the unit vector is positive elsewhere. If we need to find the unit vector in the opposite direction of the given vector then the sign of the unit vector will be negative.

Given,

Vector is$\widehat i + \widehat j + \widehat k$. Now, we need to find the unit vector in the direction of $\widehat i + \widehat j + \widehat k$. As, we know that a unit vector is given by dividing the vector by its magnitude, so the resulting vector has magnitude 1and is in same direction as the original vector.

Let$\widehat a = \widehat i + \widehat j + \widehat k$, Now magnitude of $\widehat a$is

\[\begin{gathered}

\Rightarrow \left| {\widehat a} \right| = \sqrt {{1^2} + {1^2} + {1^2}} \\

\Rightarrow \left| {\widehat a} \right| = \sqrt 3 \\

\end{gathered} \]

As, we know the unit vector in the direction of $\widehat a $ is $\dfrac{{\widehat a}}{{\left| {\widehat a} \right|}}$.Now, the unit vector in the direction of $\widehat i + \widehat j + \widehat k$ will be

$ \Rightarrow \dfrac{{\widehat i + \widehat j + \widehat k}}{{\sqrt 3 }}$

Therefore, the unit vector in the direction of $\widehat i + \widehat j + \widehat k$ is $\dfrac{{\widehat i + \widehat j + \widehat k}}{{\sqrt 3 }}$.

Hence, the required option for the given question is ‘A’.

Note: Here, we have been asked to find the unit vector in the direction of the vector, hence the sign of the unit vector is positive elsewhere. If we need to find the unit vector in the opposite direction of the given vector then the sign of the unit vector will be negative.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

How do you graph the function fx 4x class 9 maths CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths