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Q: Why the addition of vector A and B is equal to 0?

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Depends on the situation. Vector A x Vector B= 0 when the sine of the angle between them is 0 Vector A . Vector B= 0 when the cosine of the angle between them is 0 Vector A + Vector B= 0 when Vectors A and B have equal magnitude but opposite direction.

It's impossible as the addition of two vectors is commutative i.e. A+B = B+A.For subtraction of two vectors, you have to subtract a vector B from vector A.The subtraction of the vector B from A is equivalent to the addition of (-B) with A, i.e. A-B = A+(-B).

The zero vector is both parallel and perpendicular to any other vector. V.0 = 0 means zero vector is perpendicular to V and Vx0 = 0 means zero vector is parallel to V.

1. When the two vectors are parlell the magnitude of resultant vector R=A+B. 2. When the two vectors are having equal magnitude and they are antiparlell then R=A-A=0. For more information: thrinath_dadi@yahoo.com

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

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.

90 degrees

If the vectors a and b are arranged so that the head of a (the arrow bit) is at the tail of b, then c must be from the tail of a to the head of b. The vectors a and b can be swapped since vector addition is commutative.

When b is zero.

In addition of vector when vector A whose head is joined to the tail of the vector B and then the tail of the vector A is linked with the tail of the resultant vector and the head of the vector B is joined with the head of the resultant vector..... it means the addition of vectors are also defined the head to tail rule..

Regular Math Addition: 432+53=485 Vector Addition: if u=<a,b> and v=<c,d> then u+v=<a+c,b+d>

B could be either greater than, lesser than or equal to A. 7 +(-7) = 0 (-7) = 7 = 0 0 + 0 = 0

C equals A plus B under all circumstances; C= A + B.

Vector addition derives a new vector from two or more vectors. The sum of two vectors, A = (a, b) and B = (c,d), is given as S = A+B = (a+c, b+d). Vector resolution should be called something like vector decomposition. It is simply the operation of taking a vector A and writing the components of that vector, (a,b). It's very easy to determine the horizontal and vertical component vectors using trigonometric identities. The vector A starts at the origin and ends at a point (a, b), vector resolution is the method for determining a and b. The lengths a and b can be computed by knowing the length of the original vector A (the magnitude or A) and the angle from the horizontal, theta: a = A*cos(theta), b = A*sin(theta). Going in the other direction, the vector A can be reconstructed knowing only a and b. The magnitude is given by A = sqrt(a*a + b*b). The angle theta is given by solving cos(theta) = a/A (or sin(theta) = b/A). And, in fact, if you take the component vectors a and b, their sum gives the original vector, A = a + b, where a should be thought of as a*i and b = b*j where i and j are unit vectors in x and y directions.Vector addition is when you add two or more vectors together to create a vector sum.

If 'A' and 'B' are vectors, and their magnitudes are equal, andtheir directions are opposite, then their vector sum is zero.

(A1) The dot product of two vectors is a scalar and the cross product is a vector? ================================== (A2) The cross product of two vectors, A and B, would be [a*b*sin(alpha)]C, where a = |A|; b = |B|; c = |C|; and C is vector that is orthogonal to A and B and oriented according to the right-hand rule (see the related link). The dot product of the two vectors, A and B, would be [a*b*cos(alpha)]. For [a*b*sin(alpha)]C to equal to [a*b*cos(alpha)], we have to have a trivial solution -- alpha = 0 and either a or b be zero, so that both expressions are zeroes but equal. ================================== Of course one is the number zero( scalar), and one is the zero vector. It is a small difference but worth mentioning. That is is to say if a or b is the zero vector, then a dot b must equal zero as a scalar. And similarly the cross product of any vector and the zero vector is the zero vector. (A3) The magnitude of the dot product is equal to the magnitude of the cross product when the angle between the vectors is 45 degrees.

2pi/3 radian or equivalent 120 degree

Addition does. Subtraction, just as with numbers: a - b is not equal to b - a, but you can change a - b to -b + a.Addition does. Subtraction, just as with numbers: a - b is not equal to b - a, but you can change a - b to -b + a.Addition does. Subtraction, just as with numbers: a - b is not equal to b - a, but you can change a - b to -b + a.Addition does. Subtraction, just as with numbers: a - b is not equal to b - a, but you can change a - b to -b + a.

In the equation a x b = 0, either a, b, or both equal zero, and there are no exceptions.

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...

No. It is the same as when you subtract normal numbers. a - b is not the same as b - a. However, if you convert the subtraction to an addition, you can use the commutative law - both with normal subtraction and with vector subtraction. That is, a - b, which can be written as a + (-b), is the same as -b + a.

0 is the identity element with regard to addition.

Element by element. That is: Sum all the first elements to get the first element of the result; Sum all the second elements to get the second element of the result...The vector sum is obtained by adding the two quantities. The vector difference is obtained by subtracting one from the other. Hint: 'sum' always means addition is involved, 'difference' always means subtraction is involved.* * * * *That is the algebraic answer. There is also a geometric answer.To sum vectors a and b, draw vector a. From the tip of vector a, draw vector b. Then a + b is the vector from the base of a to the tip of b. To calculate a - b, instead of drawing b,draw the vector -b, which is a vector of the same magnitude as b but going in the opposite direction.

(Magnitude of the vector)2 = sum of the squares of the component magnituides Let's say the components are 'A' and 'B', and the magnitude of the vector is 'C'. Then C2 = A2 + B2 You have said that C = A, so C2 = C2 + B2 B2 = 0 B = 0 The other component is zero.

public static void transpose(int[][] a, int[][] b, int width, int height) { for (int i = 0; i < width; i++) { for (int j = 0; j < height; j++) { b[j][i] = a[i][j]; } } } template <class T> void transpose( std::vector< std::vector<T> > a, std::vector< std::vector<T> > b, int width, int height) { for (int i = 0; i < width; i++) { for (int j = 0; j < height; j++) { b[j][i] = a[i][j]; } } }