Final answer:
The equation ax=b is not a vector equation; this is false. A vector equation involves vectors and can show operations such as scalar multiplication. It is true that vectors can form right-angled triangles with their components, and every 2-D vector can be expressed as the sum of its x and y components.
Step-by-step explanation:
The statement that "The equation ax=b is referred to as a vector equation" is false. A vector equation typically involves two vectors equated to each other and often includes operations like vector addition or scalar multiplication. For example, if we multiply a vector A by a scalar a, the result is a new vector B that is parallel to A, denoted as B = αA.
Concerning the properties of vectors, it is true that a vector can form the shape of a right angle triangle with its x and y components. This is due to the fact that the components of a vector are orthogonal projections onto the respective axes, and thus, when dealing with a two-dimensional vector A, we can think of Ax and Ay as forming a right angle triangle with A as the hypotenuse, if Ax and Ay are perpendicular. The length or magnitude of A can be computed using the Pythagorean theorem when Ax and Ay are at right angles to each other.
Moreover, every 2-D vector can indeed be expressed as the sum of its x and y components. For a vector A with components Ax and Ay, the vector can be written in component form as A = Axİ + AyĴ. Here, Ax and Ay are the scalar components of the vector, which can also be obtained by subtracting the origin point coordinates from the end point coordinates.