Final answer:
The statement that a vector in a plane can be the resultant of two component vectors is true. These component vectors are the orthogonal projections on the x and y axes of a Cartesian coordinate system, and their sum determines the resultant vector.
Step-by-step explanation:
The statement that every vector lying in a plane is the resultant of the sum of two special vectors called component vectors is true. In a plane, any vector can indeed be resolved into two orthogonal component vectors, often chosen to lie along the x and y axes of a Cartesian coordinate system. The x-component (∞x) and y-component (∞y) are the projections of the vector onto the respective axes. Using these components, one can apply vector algebra to find the resultant vector by simply adding the corresponding components of the vectors.
For example, if vector A has components Ax and Ay, and vector B has components Bx and By, the resultant vector R can be calculated using Rx = Ax + Bx and Ry = Ay + By. The magnitude of the resultant vector, when the components are at right angles, can be found using the Pythagorean theorem.
Also, the direction of the resultant vector depends on both the magnitude and direction of the added vectors. Moreover, knowing only the angles of the vectors without their magnitudes does not allow us to find the precise angle of the resultant vector. Finally, two vectors can form the shape of a right angle triangle with their x and y components, supporting the Pythagorean relationship between the lengths of the sides.