Final answer:
To find if the intersection of vectors A and B forms a right angle, calculate the dot product of the vectors, divided by the product of their magnitudes, and take the inverse cosine of the result. If the angle is 90 degrees, they intersect at a right angle.
Step-by-step explanation:
The question is asking to determine the angle between two vectors – vector A and vector B – and whether they form a right angle. Given vectors A and B with their magnitudes and angles with the horizontal, we can use trigonometric methods to find the resultant vector when they are added together. The components of vector A in the x and y directions (αx and αy, respectively) and those of vector B (βx and βy) can be calculated using sine and cosine functions. You can then add the respective components to find the resultant vector. By the end of this process, you can determine the angle between vector A and vector B by taking the inverse cosine of the dot product of the two vectors divided by the product of their magnitudes. If the angle is 90 degrees, the vectors form a right angle.