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

When we multiply the vector by -2, we get a new vector of magnitude, twice the magnitude of original vector. The direction is opposite to that of the original vector as the sacalar has a negative sign. 
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Can we always add two vectors? Explain your answer.


If both the vectors are of the same type, then we can add those quantities. We cannot add two different types of vector. 

For example, velocity vector and displacement vector cannot be added. 
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State polygon law of vector addition.

Polygon law of vector addition states that if two or more vectors are represented by adjacent sides of a polygon, taken in same order both in magnitude and direction, then the resultant is given by closing side of the polygon taken in opposite order both in magnitude and direction. 
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#6 {main}</pre> is multiplied by scalar k. Is the magnitude of new vector straight k space open vertical bar straight A with rightwards arrow on top close vertical bar?


No, because magnitude of a vector is positive quantity.

If is a negative scalar then  will be negative which is not possible.

The magnitude of new vector will be 

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Which of the following is true or false? Give examples: 
(i) A scalar quantity can never take negative values.
(ii) It is necessary for a scalar quantity to be dimensionless. 


(i) False, work is a scalar quantity and can have negative values. 

(ii) False, work is a scalar quantity and have dimensions.

The dimensional formula of work is M1 L2 T-2]

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