suneyna said:Now I want to ask you that is it possible that two 3d vectors pointing downwards (but both didn't lie in the same plane) can have their resultant in upward direction.
To calculate the magnitude of a 3D vector resultant, you need to use the Pythagorean theorem, which states that the square of the magnitude is equal to the sum of the squares of the individual components. In other words, you need to square the x, y, and z components of the vector, add them together, and then take the square root of the result.
A scalar quantity is a physical quantity that has only magnitude, such as mass or temperature. On the other hand, a vector quantity has both magnitude and direction, such as velocity or force. In the context of 3D vector resultant, the magnitude represents the scalar quantity, while the direction represents the vector quantity.
To calculate the direction of a 3D vector resultant, you need to use trigonometry. First, find the angles between the resultant vector and each of the three axes (x, y, and z). Then, use a trigonometric function, such as tangent or cosine, to determine the direction of the resultant vector.
Yes, a 3D vector resultant can have a negative magnitude. This occurs when the individual components of the vector have opposite signs, such as a positive x-component and a negative y-component. In this case, the resultant vector will have a negative magnitude and will be directed towards the negative quadrant of the coordinate system.
Calculating a 3D vector resultant is important in many scientific and engineering applications. It allows us to combine multiple vectors into a single vector and determine its overall magnitude and direction. This is particularly useful in fields such as physics, mechanics, and computer graphics, where vector operations are commonly used to model and analyze physical systems.