Final answer:
To find a vector perpendicular to others, identify the vectors and their context, establish a coordinate system, and calculate its perpendicular components. Apply trigonometric equations to find the components independently useful in many physics scenarios. Reassemble the vector from its components using appropriate mathematical equations.
Step-by-step explanation:
To find a non-zero vector perpendicular to other vectors, we first need to identify the vectors in question. The context provided suggests that we are analyzing a vector by breaking it down into its perpendicular components, such as the x- and y-components in a two-dimensional space.
The first step is to establish a coordinate system, typically choosing one axis to be horizontal (x-axis) and the other vertical (y-axis). Then, the perpendicular components of vector A, for instance, can be found using equations Ax = A cos θ and Ay = A sin θ, where θ is the angle vector A makes with the x-axis. These components are independent in many physics applications, such as projectile motion, making analysis more straightforward.
To reassemble vector A from its perpendicular components, utilize equations A = √(Ax² + Ay²) and θ = tan¹(Ay/Ax). This method is essential for analytical approaches to vector addition and subtraction.