You might already have come across the term vector. A quantity which has magnitude, as well as direction, is represented by a vector. The most common example of a vector in mathematics is a directed line segment. Let us say that a line AB, 5 cm in length, is pointed towards the south. In this case, AB is a vector.
In Maths, there are different types of vectors. Basic mathematical operations can be applied to them as well. In this article, we will talk about a vector which joins two points.
Equation of Vectors Joining Two Point
We can represent a point by its x coordinate, y coordinate and z coordinate. Let us say there are two points represented by their x-, y- and z- coordinates as:
We join the points P1 and P2 by a vector and call it as P1P2.
We represent the vectors from the origin O along the x-, y- and z-axes as i, j and k respectively. Now we join the origin O to P1 with the vector OP1 and to P2 with the vector OP2. Using the triangle law, we get:
Thus, the above equation represents the vector P1P2. Its magnitude can be given by:
Question 1: Find the vector and its magnitude which joins the point A with coordinates (4, 5, 6) to point B with coordinates (10, 11, 12).
Solution: The vector is directed from the point A to B and can be denoted by
Magnitude can be given by:
Question 2: Find the vector joining the points P(1, 2, 3) and Q(6, 5, 4) directed to Q from P.
The vector which is directed from the point P to Q can be written as
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