Can we multiply a vector by a scalar?

On multiplying a vector by a scalar, we get another vector whose magnitude is equal to the modulus of scalar times the magnitude of vector. The direction of the resultant vector is either same or opposite as that of vector depending upon whether scalar is positive or negative, respectively. 
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Pick up the scalar and vector quantities out of the following quantities: mass, force, temperature, displacement, frequency, surface energy, current, electric field, gravitational field. 

Vector quantities are force, displacement, electric field, gravitational field.

Scalar quanties are mass, temperature, frequency, surface energy, current.

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If we multiply the vector by +2, then what will be the new vector?


On multiplying the vector by +2, we get the new vector whose magnitude is twice the magnitude of original vector. Direction is same as that of the original vector because the sign of the scalar is positive. 
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Define unit vector and write the unit vector in direction of straight A with rightwards arrow on top.


A unit vector is whose magnitude is unity.

Let  be any vector whose magnitude is A.

Unit vector in direction of  is represented by  and is  given by, 
 
                         

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Do you think that if any quantity has direction, necessarily be a vector? Give example in support of your answer.

No, direction is not the only condition for a quantity to be a vector. In addition, the vector axioms should be followed by the physical quantity. 

For example, current possesses the direction even then it is a scalar because current does not follow the axiom vector addition. 
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