Final answer:
The statement is false; perpendicular lines intersect at a 90-degree angle, not 30 degrees. Perpendicularity is fundamental in vector analysis, and two vectors are perpendicular if they form a right angle and their dot product is zero.
Step-by-step explanation:
The statement that perpendicular lines consist of two intersecting lines that form a 30-degree angle is false. Perpendicular lines are defined as two lines that intersect at a 90-degree angle, also known as a right angle. Any other angle of intersection does not qualify as perpendicular.
When it comes to vectors, we use perpendicular axes to decompose vectors into their x and y components using the equations Ax = A cos and Ay = A sin. If we have two vectors that are perpendicular, their dot product will be zero since they form a 90-degree angle between each other, thus making them orthogonal vectors.
To further understand the concept, we can look at the Pythagorean theorem, which allows us to calculate the length of the resultant vector when two vectors are at right angles to each other. Indeed, a vector can form the shape of a right-angled triangle with its x and y components, which signifies the true essence of perpendicularity in vector analysis.