Final Answer:
To find a line perpendicular to a vector in 3D, the vector should have a direction opposite to the original vector. Therefore, the correct (option is B) Opposite direction.
Step-by-step explanation:
In three-dimensional space, a vector is defined by three components (x, y, z). For a given vector V = [a, b, c], a vector perpendicular to it can be found by swapping the signs of any two components. For example, a vector perpendicular to V could be W = [-b, a, c]. This new vector has the opposite direction to V, making the correct option for finding a line perpendicular to a vector in 3D ""Opposite direction"" (Option B).
Understanding vector properties is essential in various fields, including physics and computer graphics. The concept of finding a vector perpendicular to another vector is crucial for determining orthogonal directions in three-dimensional space. This process is widely used in applications such as computer graphics, where perpendicular vectors are employed for lighting calculations and shading.
In conclusion, finding a line perpendicular to a vector involves selecting a vector with an opposite direction. This choice ensures orthogonality, a fundamental concept in vector algebra, providing a basis for understanding spatial relationships and enhancing problem-solving capabilities in three-dimensional scenarios.