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How does the angle vectors affect the resultant vector?
The angle between two vectors significantly influences the magnitude and direction of the resultant vector. When two vectors are aligned in the same direction, their magnitudes simply add up, resulting in a larger resultant vector. Conversely, if they are at an angle to each other, the resultant vector's magnitude can be calculated using the cosine rule, and its direction is determined by the vector addition process. The greater the angle between the vectors, the more the resultant vector's magnitude can be diminished.
How angle between vectors affects the resultant?
The Law of Cosines shows the affect of the angle between vectors. R^2 = (A+B)(A +B)*= (AA* + BB* + 2ABcos(AB)) If the angle is less than 90 degrees the resultant squared R^2 is greater than the sum of the vectors squared. If the angle is 90 degrees the resultant squared is the sum of the vectors squared. If the angle is greater than 90 degrees, the resultant squared is less than the Sum of the vectors squared.
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.
What is the commutive property of a addition?
According to the commutative property of addition, the order of the addends does not affect the result. Thus, A + B = B + A
How are associative and commutative proerties alike and different?
They are alike in so far as they are properties of binary operations on elements of sets. T The associative property states that order in which operations are evaluated does not affect the result, while the commutative property states that the order of the operands does not make a difference. Basic binary operators are addition, subtraction, multiplication, division, exponentiation, taking logarithms. Basic operands are numbers, vectors, matrices.
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.
How angle between vectors affects the resultant?
The Law of Cosines shows the affect of the angle between vectors. R^2 = (A+B)(A +B)*= (AA* + BB* + 2ABcos(AB)) If the angle is less than 90 degrees the resultant squared R^2 is greater than the sum of the vectors squared. If the angle is 90 degrees the resultant squared is the sum of the vectors squared. If the angle is greater than 90 degrees, the resultant squared is less than the Sum of the vectors squared.
How does the order that the vectors are combined affect the displacement?
The order in which vectors are combined affects the overall displacement because vector addition is not commutative. The resultant vector will be different depending on the direction and magnitude of each individual vector. To find the total displacement, you must consider both the direction and magnitude of each vector in relation to the others.
How is the resultant displacement affected when 2 displacement vectors are added in a different order?
Assuming your talking about simple math of vectors, each vector is made up of components in different directions and magnitudes. Vector=V=ui+vj+wk Where i is the unit vector in the x direction, v is in the y direction, and k is in the z direction. u,v,w are the components each of these directions. If North is in the y direction and East is in the x direction, then a person traveling at 50 mi/h in the Northeast direction would have a Velocity in both i and j direction V=ui+vj Where 50mi/h=25*sqrt(25)i+25*sqrt(25)j V=sqrt{[25*sqrt(25)i]^2+[25*sqrt(25)j]^2}=50 All of this said, you simply add the components of the two vectors together, i's plus i's and j's plus j's.
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.
What are forces vectors and how do they affect the motion of objects?
Force vectors are quantities that have both magnitude and direction, representing the push or pull on an object. They affect the motion of objects by changing their speed, direction, or both. Forces can cause objects to accelerate, decelerate, change direction, or remain at rest.
Will changing the order of your displacements in the vector diagram affect magnitude and direction?
No, changing the order of displacements in a vector diagram does not affect the magnitude or direction of the resultant displacement. The resultant displacement depends only on the initial and final positions, not the order in which the displacements are added.
How can social influences affect consumption?
Social influences such as advertising affect consumption by creating a perceived need. With the perceived need, the resultant action can be spending even when there is a reduction in expendable income.
How does a change in velocity vectors affect the motion of an object?
A change in velocity vectors affects the motion of an object by altering its speed and/or direction of movement. This change can result in the object speeding up, slowing down, changing direction, or a combination of these effects.
How will the addition of water affect the acidity of a highly acidic solution having pH?
The addition of water can affect the acidity of a highly acidic solution in one major way. This addition will bring the pH up closer to 7.
How does the value of the dot product of two vectors vary based on the specific coordinate system being utilized?
The value of the dot product of two vectors can vary based on the specific coordinate system being used because the dot product is calculated by multiplying the corresponding components of the vectors and adding them together. Different coordinate systems may have different ways of representing the components of the vectors, which can affect the final value of the dot product.
What is the associative property of addition?
the associative property of addition means that changing the grouping of the addends doesn't affect the sum
