In Exercises 21–38, let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find each specified vector or scalar. v - u

Key Concepts

Vector Subtraction

Vector subtraction involves finding the difference between two vectors by subtracting their corresponding components. For vectors u = ai + bj and v = ci + dj, the result of v - u is given by (c - a)i + (d - b)j. This operation is essential for determining the relative position or direction between two vectors in a Cartesian plane.

Component Form of Vectors

Vectors in two-dimensional space can be expressed in component form as a combination of unit vectors i and j, where i represents the x-direction and j represents the y-direction. For example, the vector u = 2i - 5j has a horizontal component of 2 and a vertical component of -5. Understanding this representation is crucial for performing vector operations like addition and subtraction.

Resultant Vector

The resultant vector is the vector that results from the addition or subtraction of two or more vectors. In the case of vector subtraction, the resultant vector indicates the direction and magnitude of the difference between the two original vectors. This concept is fundamental in physics and engineering, where understanding the net effect of multiple forces or movements is necessary.