physicsss said:Could you show me an example? (maybe find the angle a 3-d vector (doesnt have to be mine) makes with the x-axis?)
Your vector is:physicsss said:i is the x-component, j is the y-com, and k is the z-com.
The vector V represents a displacement in three-dimensional space, with a magnitude of 36 units in the x-direction, 24 units in the y-direction, and 57 units in the z-direction.
The magnitude of vector V can be calculated using the Pythagorean theorem, where the magnitude is equal to the square root of the sum of the squares of the individual components. In this case, the magnitude of vector V is approximately 69.78 units.
The direction of vector V can be determined by finding the angles between the vector and each of the coordinate axes. In this case, the direction of vector V is approximately 35.54 degrees from the positive x-axis, 35.54 degrees from the positive y-axis, and 124.46 degrees from the positive z-axis.
Vector V can be represented in unit vector notation as V = 36i + 24j - 57k = 69.78(cos 35.54° i + cos 35.54° j + cos 124.46° k).
Yes, vector V can represent a physical quantity such as displacement, velocity, or force, depending on the context in which it is being used. For example, if vector V represents a displacement, its units would be in meters (m).