Final answer:
To find the scalar products of vectors when the +x-axis is horizontal to the right, you resolve each vector into its horizontal and vertical components using cosine and sine with the vector's angle, and then perform the dot product by multiplying corresponding components.
Step-by-step explanation:
Finding Scalar Products of Vectors:
To find the scalar product (also known as the dot product) of two vectors, we need to know the components of each vector. Assuming that the +x-axis is horizontal and to the right, vectors can be expressed in component form (e.g., Ax, Ay). The scalar product of two vectors A and B, with components Ax, Ay and Bx, By respectively, is found by multiplying their corresponding components and adding the results: A · B = Ax × Bx + Ay × By.
For the given problem, we must resolve the vectors into their scalar components along the x-axis and y-axis using trigonometry. We can use the relationships Ax = A · cos(θ) and Ay = A · sin(θ), where θ is the angle the vector makes with the +x-axis.
Once the vectors are resolved into components, the scalar products (a) Â · Ā, (b) Â · F, (c) Ā · Č can be found by multiplying the corresponding horizontal and vertical components for each pair of vectors and adding the results.