1)Discuss the properties of scalar product's. 2) Define gross error?
Answers
Explanation:
a)The scalar product is commutative. The two manually perpendicular vectors of a scalar product are zero. The two parallel and vectors of a scalar product are equal to the product of their magnitudes. The square of its magnitude is equal to the Self-product of a vector.
b) Gross errors are mistakes that make the measurement very far off of the known/accepted value. For example, if you were supposed to get the mass of a baseball and you chose a softball from the table to mass, that's a gross error that will skew your results.
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Scalar product of two vectors:
The scalar product of two vectors is defined by multiplying their magnitudes with the cosine of the angle between them. The scalar product of orthogonal vectors vanishes and the antiparallel vectors are negative.
Characteristics of Scalar product of two vectors:
The scalar product is commutative.
The two manually perpendicular vectors of a scalar product are zero.
The two parallel and vectors of a scalar product are equal to the product of their magnitudes.
The square of its magnitude is equal to the Self- pro duct of a vector.
Properties of the scalar product of two vectors:
The product quantity A→
⋅
B→
is always a scalar. It is positive when the angle between the vectors is acute (i.e.,<90∘
) and negative if the angle between them is obtuse (i.e.90∘<θ<180∘
).
The scalar product is commutative.
A→.B→=B→.A→.
The vectors obey distributive law.
A→.(B+C−→−−−)=A→.B→+A→.C→
The angle between the vectors,
θ=cos−1⎡⎣A⋅B−→−−AB⎤⎦
Note:The symbol for the scalar product is the dot(.) and so refers to the scalar product as the dot product.
The combining of two vectors to produce the result is scalar.
Finding the component of a vector in the direction of another vector by using the scalar product.