Vector Subtraction Calculator

Formula

The formula to calculate the new vector from the subtraction of one vector from another is:

\[ X3, Y3, Z3 = X1 - X2, Y1 - Y2, Z1 - Z2 \]

Where:

\(X3, Y3, Z3\) are the coordinates of the new vector
\(X1, Y1, Z1\) are the coordinates of the first vector
\(X2, Y2, Z2\) are the coordinates of the second vector

Vector Subtraction Definition

Vector subtraction is a mathematical operation that involves finding the difference between two vectors. It is performed by subtracting the corresponding components of the vectors. When two vectors are subtracted, their magnitudes and directions are taken into account. The resulting vector, known as the difference vector, represents the change or displacement between the initial and final positions of an object. In physics, it is used to analyze the motion of objects and calculate their displacement, velocity, and acceleration. In engineering, vector subtraction is essential for solving problems involving forces or velocities.

Example Calculation 1

Let's assume the following values:

\(X1 = 5\), \(Y1 = 7\), \(Z1 = 3\)
\(X2 = 2\), \(Y2 = 1\), \(Z2 = 4\)

Using the formula:

\[ X3 = 5 - 2 = 3 \] \[ Y3 = 7 - 1 = 6 \] \[ Z3 = 3 - 4 = -1 \]

The new vector is \((3, 6, -1)\).

Example Calculation 2

Let's assume the following values:

\(X1 = 10\), \(Y1 = 15\), \(Z1 = 20\)
\(X2 = 5\), \(Y2 = 7\), \(Z2 = 8\)

Using the formula:

\[ X3 = 10 - 5 = 5 \] \[ Y3 = 15 - 7 = 8 \] \[ Z3 = 20 - 8 = 12 \]

The new vector is \((5, 8, 12)\).