Vector Equation To Matrix Equation
What Is the Vector Equation of a Line?
The vector equation of a line is r = a + tb. In this equation, "a" represents the vector position of some point that lies on the line, "b" represents a vector that gives the management of the line, "r" represents the vector of whatever general bespeak on the line and "t" represents how much of "b" is needed to get from "a" to the position vector.
Vectors provide a simple fashion to write downwardly an equation to determine the position vector of any point on a given straight line. In order to write down the vector equation of any straight line, two known values must be present.
If the position vector of a specific point that lies on the line and a vector that gives the direction of the line, chosen a direction vector, are both present, then the position vector referred to as "r" of any general bespeak P on the line is given past the equation: r = a + tb.
For instance, suppose that Line A has the equation r = i + 3k + t(2i + j + thousand), and then that line A is i + 3k and line B is 2i + j + k. Dissimilar values of "t" provide vectors at unlike points on the line:
Putting t = 0 gives r = i + 3k.
Putting t = 1 gives r = 3i + j + 4k.
Putting t = -i gives r = -i – j + 2k.
Vector Equation To Matrix Equation,
Source: https://www.reference.com/world-view/vector-equation-line-de066b7d5555cbbf?utm_content=params%3Ao%3D740005%26ad%3DdirN%26qo%3DserpIndex&ueid=b7b28405-bcd2-4d8e-96c7-870419879437
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