Vectors in XY plane

At the XY plane, the letter i denotes the x-axis unit vector and the letter j the y-axis unit vector. These are xy-plane basis vectors.

All XY plane vectors can be expressed by the base vectors i and j.

When vectors are summed, parallel components are summed.

Example 1

We find the sum of vectors a and b below

Example 2

Find the length of the vector a

There is a formula for the length of the vector that can be found in the MAOL tables. The formula is formed from the Pythagorean theorem. The components of the vector form the catheters of a right triangle and the vector is hypotenuse.

Example 3

Find the vector from point (2,3) to point (4,6)

Let the vector be denoted by the letter a. The x-direction distance of the points (2,3) and (4,6) is 2 and the y-direction distance is 3.

Position vector

A position vector is a vector placed at a point from the origin. Below are the position vectors of points A (-3,2), B (1,4) and C (4,3). Since the position vector starts from the origin, the components are seen directly from the endpoints. For example, the distance from the origin to the point (4,3) is along the x-axis 4 and along the y-axis 3.

Position vectors

Example 4

From point A(1,3) we use the vector a to go to point B. Find coordinates of point B.

We find position vector for point B.

Now we have

So point B is (4,6)

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