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Unit vectors are perpendicular. Their dot product is zero. That means that no unit vector has any component that is parallel to another unit vector.

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Q: Dot product of unit vectors of cartesian and cylindrical coordinate system?
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What is the difference between coplanar vectors and collinear vectors?

The term collinear is used to describe vectors which are scalar multiples of one another (they are parallel; can have different magnitudes in the same or opposite direction). The term coplanar is used to describe vectors in at least 3-space. Coplanar vectors are three or more vectors that lie in the same plane (any 2-D flat surface).


What is it when two vectors' dot product is one?

That fact alone doesn't tell you much about the original two vectors. It only says that (magnitude of vector-#1) times (magnitude of vector-#2) times (cosine of the angle between them) = 1. You still don't know the magnitude of either vector, or the angle between them.


What is the difference between the ''dot product'' and the ''cross product''?

Dot Product:Given two vectors, a and b, their dot product, represented as a ● b, is equal to their magnitudes multiplied by the cosine of the angle between them, θ, and is a scalar value.a ● b = ║a║║b║cos(θ)Cross Product:Given two vectors, a and b, their cross product, which is a vector, is represented as a X b and is equal to their magnitudes multiplied by the sine of the angle between them, θ, and then multiplied by a unit vector, n, which points perpendicularly away, via the right-hand rule, from the plane that a and b define.a X b = ║a║║b║sin(θ)n


If ab then ba?

If these are vectors, then ba = - ab


How do you find the area of a parallelogram using 2 vectors?

Given two vectors a and b, the area of a parallelogram formed by these vectors is:a x b = a*b * sin(theta) where theta is the angle between a and b, and where x is the norm/length/magnitude of vector x.

Related questions

Does the scalar product of two vectors depend on the choice of coordinate system?

No.


What are the cartesian base vectors in mathematics?

They are unit vectors in the positive directions of the x and y axes.


How do you do rotation in math?

A vector rotation in math is done on a coordinate plane.2D vectors can be rotated using the cross and dot product.3D vectors are rotated using matrix based quaternion math.


Can any vector be represented by two other vectors that are right angels to each others?

Yes. This is the basis of cartesian vector notation. With cartesian coordinates, vectors in 2D are represented by two vectors, those in 3D are represented by three. Vectors are generally represented by three vectors, but even if the vector was not in an axial plane, it would be possible to represent the vector as the sum of two vectors at right angles to eachother.


Can you add three unit vectors to get a unit vector does your answer change if two unit vectors are along the coordinate axes?

Yes., and their being along the coordinate axes does not change the answer.Consider the vectors: i, -i and j where i is the unit vector along the x axis and j along the y axis. The resultant of the three is j.


Why CosӨ is used in dot product?

The cosine of the angle between two vectors is used in the dot product because it measures the similarity or alignment of the vectors. The dot product calculates the product of the magnitudes of the vectors and the cosine of the angle between them, resulting in a scalar value that represents the degree of alignment or correlation between the vectors.


When are vectors said to be perpendicular?

Perpendicular means that the angle between the two vectors is 90 degrees - a right angle. If you have the vectors as components, just take the dot product - if the dot product is zero, that means either that the vectors are perpendicular, or that one of the vectors has a magnitude of zero.


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.


1 For the two vectors find the scalar product AB and the vector product?

For two vectors A and B, the scalar product is A.B= -ABcos(AB), the minus sign indicates the vectors are in the same direction when angle (AB)=0; the vector product is ABsin(AB). Vectors have the rule: i^2= j^2=k^2 = ijk= -1.


Why the product of two vectors is sometime scalar and sometime vector?

Because there are two different ways of computing the product of two vectors, one of which yields a scalar quantity while the other yields a vector quantity.This isn't a "sometimes" thing: the dot product of two vectors is always scalar, while the cross product of two vectors is always a vector.


What are the operation on vector?

That really depends on the type of vectors. Operations on regular vectors in three-dimensional space include addition, subtraction, scalar product, dot product, cross product.


What is the difference between orthogonal and orthonormal vectors?

All vectors that are perpendicular (their dot product is zero) are orthogonal vectors.Orthonormal vectors are orthogonal unit vectors. Vectors are only orthonormal if they are both perpendicular have have a length of 1.