If the magnitude of the sum of two vectors is greater than the magnitude of either vector, then scaler product will always be positive
A vector is a quantity or phenomenon that has two independent properties: magnitude and direction. The term also denotes the mathematical or geometrical representation of such a quantity.
The scalar product of two vectors is the sum of the product of the corresponding components of the vectors. In other words, the scalar product is equal to the product of the magnitudes of the two vectors and the cosine of the angle between them. It is a scalar quantity and is also called the dot product of vectors.
if | a + b | > |a| or |b|
a. b = |a| |b| cos (theta)
since , | a + b | > |a| or |b|
hence, angle between a and b must be less than 90°
since , |a| and |b| are positive
cos (theta ) will also be positive as angle is between 0° and 90°
hence , cos (theta ) will be positive
hence scaler product will always be positive
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