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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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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.
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.
Does the scalar product of two vectors depend on the choice of coordinate system?
No.
Why dot product of two vectors is scalar?
That's the way it is defined.
What is the value of scalar product of two vectors A and B where value of vector A and B is not zero and vector product of two vectors A and B is not zero?
Scalar product = (magnitude of 'A') times (magnitude of 'B') times (cosine of the angle between 'A' and 'B')
Can the scaler product of two vectors be negetiv if the answer is yes provid a proof and given exampl?
Yes, for example the vectors <1, 0> and <-1, 0>. In general, if the angle between the two vectors is more than 90 degrees (or pi/2 radians), the scalar product is negative.
1 For the two vectors find the scalar product AB and the vector product?
For two vectors A and B, the scalar product is A.B= -ABcos(AB), the minus sign indicates the vectors are in the same direction when angle (AB)=0; the vector product is ABsin(AB). Vectors have the rule: i^2= j^2=k^2 = ijk= -1.
Is it possible to multiply a vector quantity to a scalar quantity?
The product of scalar and vector quantity is scalar.
What is the product of vector and scalar?
The scalar product of two perpendicular vectors is zero.In classical mechanics we define the scalar product between two vector a and b as:a · b = |a| |b| cos(alpha)where |a| is the modulus of vector a and alpha is the angle between vectors a and b.If two vectors are perpendicular, alpha equals 90º (or PI/2 rad) and cosine of alpha is, consequently, zero.So finally a · b = 0.
Who is the commutative property in dot and cross product?
The cross product results in a vector quantity that follows a right hand set of vectors; commuting the first two vectors results in a vector that is the negative of the uncommuted result, ie A x B = - B x A The dot product results in a scalar quantity; its calculation involves scalar (ie normal) multiplication and is unaffected by commutation of the vectors, ie A . B = B . A
Is there any direction associated with the dot product of two vectors?
No. The dot product is also called the scalar product and therein lies the clue.
