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What is the result of applying the s2 operator to the given function?
The result of applying the s2 operator to a function is the second derivative of the function with respect to the variable s.
What are different conditions that could make vector product zero?
First of all, you have to define what you mean by "vector product".-- The "dot product" is zero if the vectors are perpendicular, regardless of their magnitudes.-- The "cross product" is zero if the vectors are collinear or opposite, regardless of their magnitudes.-- Perhaps when you say "product", you mean the "result" of two vectors, whicha mathematician or physicist would cal their "sum".The sum of two vectors is zero if their magnitudes are equal and their directionsdiffer by 180 degrees.An infinite number of other possibilities exist for a sum of zero, depending on themagnitudes and directions of two vectors.
Can scalar product be negative?
Yes, the scalar product of two vectors can be negative if the angle between them is obtuse (greater than 90 degrees). In this case, the result of the scalar product will be negative.
Does the order of addition of indivitual vectors affect the final resultant vector and why?
The order of addition of individual vectors does not affect the final result. The reason is that "addition is commutative", meaning C=A +B = B + A. The laws of multiplication fro vectors is non-commutative and AxB = - BxA. Multiplication of vectors is non-commutative. Vectors and Reals make up our natural numbers called Quaternions . Given a quaternion A=Ar + Av where Ar is the real part of A and Av is the vector part of A and B=Br +Bv, the product is: AB=(Ar + Av)(Br + Bv)= (ArBr - Av.Bv) + (ArBv + AvBr + AvxBv) If the vectors are perpendicular Av.Bv=0, (the dot '.' denotes the cosine product). If the vectors are parallel AvxBv=0, (the cross 'x' denotes the sine product). Unfortunately quaternions multiplication is not taught in schools. Quaternions simplify algebra, trigonometry and vectors. Quaternions are also the natural numbers of the Universe.
Why does the cross product give a perpendicular vector?
The cross product gives a perpendicular vector because it is calculated by finding a vector that is perpendicular to both of the original vectors being multiplied. This property is a result of the mathematical definition of the cross product operation.
What is the result of applying the s2 operator to the given function?
The result of applying the s2 operator to a function is the second derivative of the function with respect to the variable s.
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.
What are different conditions that could make vector product zero?
First of all, you have to define what you mean by "vector product".-- The "dot product" is zero if the vectors are perpendicular, regardless of their magnitudes.-- The "cross product" is zero if the vectors are collinear or opposite, regardless of their magnitudes.-- Perhaps when you say "product", you mean the "result" of two vectors, whicha mathematician or physicist would cal their "sum".The sum of two vectors is zero if their magnitudes are equal and their directionsdiffer by 180 degrees.An infinite number of other possibilities exist for a sum of zero, depending on themagnitudes and directions of two vectors.
If a and b are two vectors and the vector product of vector a and vector b is equal to a minus b then prove that a equals b?
The question is not correct, because the product of any two vectors is just a number, while when you subtract to vectors the result is also a vector. So you can't compare two different things...
Can scalar product be negative?
Yes, the scalar product of two vectors can be negative if the angle between them is obtuse (greater than 90 degrees). In this case, the result of the scalar product will be negative.
How do you find angle btw two vectors?
To find the angle between two vectors, you can use the dot product formula: ( \cos(\theta) = \frac{\mathbf{A} \cdot \mathbf{B}}{|\mathbf{A}| |\mathbf{B}|} ), where ( \theta ) is the angle between the vectors, ( \mathbf{A} ) and ( \mathbf{B} ) are the vectors, and ( |\mathbf{A}| ) and ( |\mathbf{B}| ) are their magnitudes. First, calculate the dot product of the two vectors, then divide by the product of their magnitudes. Finally, take the inverse cosine (arccos) of the result to find the angle in radians or degrees.
How do you find the product of a fraction?
A product is a binary operator. That means a product is the result of combining TWO numbers. You cannot have a product of just one number - whether it is a fraction or not is irrelevant.
Why are some vectors pseudo vectors and some real vectors?
Answer: There are no "pseudo vectors" there are pseudo "rules". For example the right hand rule for vector multiplication. If you slip in the left hand rule then the vector becomes a pseudo vector under the right hand rule. Answer: A pseudo vector is one that changes direction when it is reflected. This affects all vectors that represent rotations, as well as, in general, vectors that are the result of a cross product.
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
Does the order of adding vectors affects the magnitude and direction of the vectors?
No. The order of adding vectors does not affect the magnitude or direction. of the result.
Does the order of addition of indivitual vectors affect the final resultant vector and why?
The order of addition of individual vectors does not affect the final result. The reason is that "addition is commutative", meaning C=A +B = B + A. The laws of multiplication fro vectors is non-commutative and AxB = - BxA. Multiplication of vectors is non-commutative. Vectors and Reals make up our natural numbers called Quaternions . Given a quaternion A=Ar + Av where Ar is the real part of A and Av is the vector part of A and B=Br +Bv, the product is: AB=(Ar + Av)(Br + Bv)= (ArBr - Av.Bv) + (ArBv + AvBr + AvxBv) If the vectors are perpendicular Av.Bv=0, (the dot '.' denotes the cosine product). If the vectors are parallel AvxBv=0, (the cross 'x' denotes the sine product). Unfortunately quaternions multiplication is not taught in schools. Quaternions simplify algebra, trigonometry and vectors. Quaternions are also the natural numbers of the Universe.
Why does the cross product give a perpendicular vector?
The cross product gives a perpendicular vector because it is calculated by finding a vector that is perpendicular to both of the original vectors being multiplied. This property is a result of the mathematical definition of the cross product operation.
