Pre-Calculus Prep: Finding the Resultant Vector NOT in Component Form

To find the resultant vector 4TX + YZ without using component form, you can use the concept of vector addition and scalar multiplication. Here's how you can do it:

1. Identify the given vectors: Let's say T, X, Y, and Z are the given vectors, represented as T = (x₁, y₁), X = (x₂, y₂), Y = (x₃, y₃), and Z = (x₄, y₄).

2. Multiply each vector by its respective scalar: Multiply vector TX by 4 and vector YZ by 1:
4TX = 4 * (X - T)
YZ = Y - Z

3. Perform vector subtraction: Subtract the corresponding components of each vector:
4TX = 4 * (x₂ - x₁, y₂ - y₁)
YZ = (x₃ - x₄, y₃ - y₄)

4. Simplify the resulting vectors: Distribute the scalar multiplication to each component:
4TX = (4 * x₂ - 4 * x₁, 4 * y₂ - 4 * y₁)
YZ = (x₃ - x₄, y₃ - y₄)

5. Add the resulting vectors: Add the corresponding components of 4TX and YZ:
Resultant vector = (4 * x₂ - 4 * x₁ + x₃ - x₄, 4 * y₂ - 4 * y₁ + y₃ - y₄)

The resulting vector represents the sum of 4TX and YZ. It combines the corresponding components of each vector after scalar multiplication and addition.

Remember to perform the operations for each component separately, combining the horizontal and vertical components to find the resultant vector.

By following these steps, you can find the resultant vector 4TX + YZ without using component form in pre-calculus.

These videos are designed to review and reteach Precalculus and Collegeboard Pre-CALC AP content. My videos cover functions, polynomials, exponential and logarithmic expressions, trigonometry, parametric equations, polar coordinates, vectors, matrices and systems, conic sections, discrete mathematics, sequences and series; and an introduction to calculus.

Nick Perich
Norristown Area High School
Norristown Area School District
Norristown, Pa .
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