# If \[\overrightarrow{a}\] is a non- zero vector of modulus a and m is a non-zero scalar, then \[m\overrightarrow{a}\] is a unit vector if

Answer

Verified

277.5k+ views

**Hint:**According to Newton’s second law of motion force is the product of mass and acceleration. Since the product m and a are unity. By rearranging them we will get the relation connecting m and \[\overrightarrow{a}\]. When we multiply a scalar with a vector quantity the resultant quantity will be a vector.

**Complete step-by-step solution:**

If we multiply a scalar with a vector quantity the resultant quantity will be a vector. Here the scalar quantity is mass and acceleration is a vector quantity. Here the vector quantity is called force.

Given that \[\overrightarrow{a}\] is a non- zero vector of modulus a and m is a non-zero scalar. Also given that product of m and a is unity. That is,

\[\left| m\overrightarrow{a} \right|=1\]

The product of mass and acceleration \[m\overrightarrow{a}\]is a unit vector only if,

\[m=\dfrac{1}{\left| \overrightarrow{a} \right|}\]

Here m becomes the reciprocal of \[\overrightarrow{a}\].

Where, \[\overrightarrow{a}\] is a non- zero vector of modulus a and m is a non-zero scalar.

**Thus the answer is \[m=\dfrac{1}{\left| \overrightarrow{a} \right|}\].**

**Note:**If we multiply a scalar with a vector quantity the resultant quantity will be a vector. Here the scalar quantity is mass and acceleration is a vector quantity. So while taking the product of those two quantities the resultant quantity is a vector. Here the vector quantity is called force. That is the product of mass and acceleration gives the force which is Newton’s second law of motion. Here the force will be unity only if m becomes the reciprocal \[\overrightarrow{a}\].

Recently Updated Pages

Basicity of sulphurous acid and sulphuric acid are

Define absolute refractive index of a medium

Which of the following would not be a valid reason class 11 biology CBSE

Why should electric field lines never cross each other class 12 physics CBSE

An electrostatic field line is a continuous curve That class 12 physics CBSE

What is meant by monosporic development of female class 11 biology CBSE

Trending doubts

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

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

How many meters are there in a kilometer And how many class 8 maths CBSE

What is pollution? How many types of pollution? Define it

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

What were the major teachings of Baba Guru Nanak class 7 social science CBSE

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

Draw a labelled sketch of the human eye class 12 physics CBSE