Can it be zero? Answer: Magnitude cannot be negative. It is the length of the vector which does not have a direction (positive or negative). The zero vector (vector where all values are 0) has a magnitude of 0, but all other vectors have a positive magnitude.

The magnitude of a vector is the length of the vector. The magnitude of the vector a is denoted as ∥a∥.

The magnitude of a vector is the length of the vector. The magnitude of the vector a is denoted as ∥a∥. See the introduction to vectors for more about the magnitude of a vector. For a two-dimensional vector a=(a1,a2), the formula for its magnitude is ∥a∥=√a21+a22. …

Yes, two vectors of equal magnitude that are pointing in opposite directions will sum to zero. Two vectors of unequal magnitude can never sum to zero. If they point along the same line, since their magnitudes are different, the sum will not be zero.

The cross product is always orthogonal to both vectors, and has magnitude zero when the vectors are parallel and maximum magnitude ‖a‖‖b‖ when they are orthogonal.

The Cross Product gives a vector answer, and is sometimes called the vector product. But there is also the Dot Product which gives a scalar (ordinary number) answer, and is sometimes called the scalar product.

When two vectors are perpendicular to each other, then the angle between them will be equal to 90 degrees. As we know, the cross product of two vectors is equal to product of their magnitudes and sine of angle between them.

The middle finger will be in direction of vector b. The thumb will show the direction of the vector. The direction of a×b is will not be same to b×a. Thus, the cross product of two vectors does not obey commutative law.

Vector addition is commutative, just like addition of real numbers. If you start from point P you end up at the same spot no matter which displacement (a or b) you take first.

The dot product of two vectors is commutative; that is, the order of the vectors in the product does not matter. Multiplying a vector by a constant multiplies its dot product with any other vector by the same constant.

Note: Cross products are not commutative. That is, u × v ≠ v × u. The vectors u × v and v × u have the same magnitude but point in opposite directions.

See what happens when you try to take (a×b)⋅a or (a×b)⋅b (you should get 0). If a vector is perpendicular to a basis of a plane, then it is perpendicular to that entire plane. So, the cross product of two (linearly independent) vectors, since it is orthogonal to each, is orthogonal to the plane which they span.

Vector Triple Product is a branch in vector algebra where we deal with the cross product of three vectors. The value of the vector triple product can be found by the cross product of a vector with the cross product of the other two vectors. It gives a vector as a result.

The magnitude of the vector product of two vectors can be constructed by taking the product of the magnitudes of the vectors times the sine of the angle (<180 degrees) between them. The magnitude of the vector product can be expressed in the form: and the direction is given by the right-hand rule.

Vector product also means that it is the cross product of two vectors. If you have two vectors a and b then the vector product of a and b is c. c = a × b. So this a × b actually means that the magnitude of c = ab sinθ where θ is the angle between a and b and the direction of c is perpendicular to a well as b.

The scalar product of two vectors is defined as the product of the magnitudes of the two vectors and the cosine of the angles between them.

Algebraically, the dot product is the sum of the products of the corresponding entries of the two sequences of numbers. Geometrically, it is the product of the Euclidean magnitudes of the two vectors and the cosine of the angle between them. These definitions are equivalent when using Cartesian coordinates.

The Dot Product gives a scalar (ordinary number) answer, and is sometimes called the scalar product. But there is also the Cross Product which gives a vector as an answer, and is sometimes called the vector product.

The dot product between a unit vector and itself is also simple to compute. Given that the vectors are all of length one, the dot products are i⋅i=j⋅j=k⋅k=1.

Two vectors are orthogonal if the angle between them is 90 degrees. Thus, using (**) we see that the dot product of two orthogonal vectors is zero. Conversely, the only way the dot product can be zero is if the angle between the two vectors is 90 degrees (or trivially if one or both of the vectors is the zero vector).

Since i,j, k represent unit vector in the direction of X,Y and Z axis respectively.

If you already know the vectors are both normalized (of length one), then the dot product equaling one means that the vectors are pointing in the same direction (which also means they’re equal). For example, 2D vectors of (2, 0) and (0.5, 0) have a dot product of 2 * 0.5 + 0 * 0 which is 1 .

An inner product is the more general term which can apply to a wide range of different vector spaces. The dot product is the name given to the inner product on a finite dimensional Euclidean space. For such a space all terms mean the same thing but it might be better to us one term or another in different contexts.