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The scaler product of two vector can be negative,if the angle b/w two vector is 180 or two vector or antiparallel to each other
A.B=ABcos
A.B=ABcos180
A.B=-AB
THIS SHOW THAT SCALER PRODUCT OF TWO VECTOR CAN BE NEGATIVE.
EXAMPLE::Work done against force of friction:w=f.d
w=fbcos
w=fbcos180
w=-fb
:Work done against gravity:
w=f.d
here f=mg and d=h
so putting value
w=mghcos
w=mghcos180
w=-mgh
HENCE WORK DONE AGAINST FORCE OF GRAVITY IS NEGATIVE
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CoachYes, the scalar product of two vectors can be negative. The scalar product, also known as the dot product, is calculated by multiplying the magnitudes of the vectors, the cosine of the angle between them, and the direction. If the angle between the vectors is obtuse (greater than 90 degrees), the cosine of the angle will be negative, resulting in a negative scalar product.
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What is the product of two vector quantities?
It depends on the type of product used. A dot or scalar product of two vectors will result in a scalar. A cross or vector product of two vectors will result in a vector.
Why is scalar product two vectors a scalar?
Scalar product of two vectors is a scalar as it involves only the magnitude of the two vectors multiplied by the cosine of the angle between the vectors.
Why the product of two vectors is sometime scalar and sometime vector?
Because there are two different ways of computing the product of two vectors, one of which yields a scalar quantity while the other yields a vector quantity.This isn't a "sometimes" thing: the dot product of two vectors is always scalar, while the cross product of two vectors is always a vector.
Why dot product of two vectors is scalar?
That's the way it is defined.
Does the scalar product of two vectors depend on the choice of coordinate system?
No.
