Can you find a vector quantity that has a magnitude of zero but components that are different from zero? Explain.
F1 = 100[30o] N. of E. = [30o]CCW.
F1 + F2 = 0.
100[30] + F2 = 0.
100*Cos30 + (100*sin30)i + F2 =0.
86.6 + 50i + F2 = 0.
F2 = -86.6-50i(Q3) = 100[30o] S. of W. = 100[210o] CCW from +x-axis.
210o - 30o = 180o. So the two vectors are 180o out of phase. Therefore, point in opposite directions and have equal magnitudes.
Yes, I can help you with that! In order to find a vector quantity that has a magnitude of zero but components that are different from zero, we need to understand the concept of vector addition or subtraction.
A vector quantity is represented by both magnitude and direction. When we add or subtract vectors, the magnitudes and directions are taken into account. The magnitude of a vector is a scalar value representing its size, while the components of a vector represent its direction.
To find a vector with zero magnitude but non-zero components, we consider the cancellation effect that occurs when two vectors of the same magnitude but opposite directions are added together. In this case, the magnitudes cancel each other out, resulting in a vector with zero magnitude.
Let's consider an example: Imagine two vectors, A and B, with equal magnitudes but opposite directions. If we add these vectors together, the magnitudes cancel each other out, resulting in a zero vector.
Now, let's assign concrete values to the components of the vectors A and B. For simplicity, let's consider 2-dimensional vectors. Suppose vector A has components (1, 0) and vector B has components (-1, 0). Both vectors have a magnitude of 1, but since their directions are opposite, when we add them together, we obtain a vector with components (1 + (-1), 0 + 0) which equals (0, 0). The resulting vector has zero magnitude, but its components are non-zero.
So, in conclusion, by adding or subtracting vectors of equal magnitude but opposite directions, we can obtain a vector with zero magnitude but non-zero components.