Let x = [x1, x2, ... xk] and y= [y1, y2, ... yk] be the two vectors of length k.
Then we define their sum to be x+y = [x1+y1, x2+y2, ... xk+yk]
In other words, add the corresponding elements in the two vectors.
There is no difference between vector addition and algebraic addition. Algebraic Addition applies to vectors and scalars: [a ,A ] + [b, B] = [a+b, A + B]. Algebraic addition handles the scalars a and b the same as the Vectors A and B
Zero vector or null vector is a vector which has zero magnitude and an arbitrary direction. It is represented by . If a vector is multiplied by zero, the result is a zero vector. It is important to note that we cannot take the above result to be a number, the result has to be a vector and here lies the importance of the zero or null vector. The physical meaning of can be understood from the following examples. The position vector of the origin of the coordinate axes is a zero vector. The displacement of a stationary particle from time t to time tl is zero. The displacement of a ball thrown up and received back by the thrower is a zero vector. The velocity vector of a stationary body is a zero vector. The acceleration vector of a body in uniform motion is a zero vector. When a zero vector is added to another vector , the result is the vector only. Similarly, when a zero vector is subtracted from a vector , the result is the vector . When a zero vector is multiplied by a non-zero scalar, the result is a zero vector.
It is an integral part of the vector and so is specified by the vector.
The components of a vector are magnitude and direction.
0 is a cross product of a vector itself
Yes.
The parallelogram law of vector addition states that if two vectors are represented as two adjacent sides of a parallelogram, the resultant vector can be obtained by drawing a diagonal from the point where the two vectors originate. Mathematically, this law can be expressed as ( R^2 = A^2 + B^2 + 2AB \cos(\theta) ), where ( R ) is the magnitude of the resultant vector, ( A ) and ( B ) are the magnitudes of the two vectors, and ( \theta ) is the angle between them. This law illustrates how vectors can be combined geometrically and is fundamental in understanding vector addition in physics and mathematics.
the opposite to vector addition is vector subtraction.
Using Gravesand's apparatus
reverse process of vector addition is vector resolution.
Vector addition is basically similar, with respect to many of its properties, to the addition of real numbers.A + B = B + ASubtraction is the inverse of addition: A - B = A + (-B), where (-B) is the opposite vector to (B).A - B is not usually the same as B - A. Therefore, it is not commutative.However, if you convert it to an addition, you can apply the commutative law: A + (-B) = (-B) + A.
The opposite of vector addition is vector subtraction, while the opposite of vector subtraction is vector addition. In vector addition, two vectors combine to form a resultant vector, whereas in vector subtraction, one vector is removed from another, resulting in a different vector. These operations are fundamental in vector mathematics and physics, illustrating how vectors can be combined or separated in different contexts.
no because triangle only contain three vectors and if many vector are added then they cant form a triangle
To determine the error between a vector addition and the real results, you would subtract the calculated vector addition from the real vector addition. This difference will provide you with the error value. The error value can then be analyzed to understand the accuracy of the vector addition calculation.
There is basically no difference. They are nothing more than 2 different visualizations of how we can graphically add two vectors.strictly if we say there is one and only difference is that---Triangle law of vector addition states that when 2 vectors r acting as the adjacent sides of a triangle taken in order. third side of the triangle will give the magnitude of th resultant 7 direction is in opposite order.Parallelogram law of vector addition states that if 2 vectors r acting as the adjacent sides of a parallelogram, then the diagonal of parallelogram from the point of intersection of two vectors represent their resultant magnitude & direction.
The term given to the net figure that results from a vector addition is the resultant vector.
Vector resolution involves breaking down a single vector into its horizontal and vertical components, while vector addition combines two or more vectors together to form a resultant vector. They are considered opposite processes because resolution breaks a single vector into simpler components, while addition combines multiple vectors into a single resultant vector.