Question

When working with vectors, you will often see right triangles. What are the consistent properties of these triangles?

a. The hypotenuse of the triangle is always the vector itself.
b. The trangles are always equilateral.
c. The sides of the triangles always ine up with the x- and y-axes.
d. The triangles always have the same base and height

Answer 1

a) and c)

Step-by-step explanation:

• Any vector can be expressed as a vector sum of its x- and -y components, as follows:

v = vₓ* x + vy* y

• where vₓ = x- component, x= unit vector in the x direction, vy = y-component, y = unit vector in the y direction.

• If we add the components graphically, using the head-to-tail method, it will be defined a right triangle, being the vector sum of both components (the vector itself) the hypotenuse of the triangle.
• As both components are perpendicular, they will be always lined up with the x- and y- axes.