Line is a geometrical shape that extends to infinity. Part of line with specific measure is called as line segment .These line segments are of a fixed length and can be used to symbolize vector magnitudes. We have studied the representation of magnitudes of vectors and only property of math vectors left is its direction which can be represented by sketching an arrow over the end of the line segment. There are several applications of vectors in subjects of sciences like physics and maths.
To solve Vectors Math problems we need to know the calculus math. So, let us study how to deal with math vectors.
There can be number of vector operations, but tasks like cross product and scalar or dot product of vectors are normally found in maths problems. The cross product would result in a new vector quantity that is orthogonal with other two vectors. Scalar product of two vectors would result in a scalar quantity. If vector is multiplied by a scalar number, a vector quantity is obtained.
Let us undertake an illustration to show how to calculate the cross product of vectors in math.
Example: Consider two vectors: A= (4, 2, 3) and B = (5, 6, 2). Find their cross product i.e. A X B.
Solution:
i |
j |
k |
4 |
2 |
3 |
5 |
6 |
2 |
Cross product is actually a binary operation on two vectors. It is also referred as vector product since result of product is also a vector quantity. Resultant vector quantity is perpendicular to both vector being multiplied. In other words, resultant vector is normal to that plane containing multiplied vectors. Cross product operates in 3-D space. Cross...Read More
Dot product is also known as scalar product. It can be defined as product of two vectors which produces a scalar quantity. Two vectors must be of similar length. It is named as dot product since symbol dot (.) is used to multiply two vectors. Dot product can be expressed by following diagram:
Here P and Q are two vectors and their dot ...Read More
Normal vector can be defined as vector which is perpendicular to given plane or it may be normal to the plane in which other vector is existing. In other words, normal vector is a vector perpendicular to surface at point O that is perpendicular to tangent plane of that surface at point O. Concept of normality is used to determine orthogonality. Normal vectors ar...Read More