A vector F1 is along the positive X axis. If its vector product wiyh a...
**Understanding Vector Product**
The vector product, also known as the cross product, is a mathematical operation that combines two vectors to produce a third vector. It is denoted by the symbol "×" or "x". When the vector product of two vectors is zero, it implies certain characteristics about the relationship between those vectors.
**The Cross Product of F1 and F2**
Let's consider a vector F1 that is along the positive X-axis. In Cartesian coordinates, F1 can be represented as:
F1 = (F1x, F1y, F1z) = (F1, 0, 0)
Now, we have another vector F2. The vector product of F1 and F2 is given by:
F1 × F2 = (F1yF2z - F1zF2y) i + (F1zF2x - F1xF2z) j + (F1xF2y - F1yF2x) k
Since F1 is along the positive X-axis, its y and z components are both zero. So, the vector product simplifies to:
F1 × F2 = 0i + 0j + 0k = 0
**Implication of a Zero Vector Product**
When the vector product of two vectors is zero, it indicates certain properties about the relationship between those vectors. In this case, it implies the following:
1. F1 and F2 are parallel or collinear: Since the vector product is zero, it means that the vectors F1 and F2 are either parallel or collinear. This means that F2 lies along the X-axis or is parallel to it.
2. F2 can be in the positive or negative X direction: While the vector product being zero implies that F2 lies along the X-axis, it does not provide information about the direction. F2 could be either in the positive X direction (same as F1) or in the negative X direction (opposite to F1).
3. F2 can have non-zero y and z components: Although the vector product is zero, it does not necessarily mean that the y and z components of F2 are zero. F2 can have non-zero y and z components as long as it lies along the X-axis.
**Conclusion**
If the vector product of vector F1, which is along the positive X-axis, and vector F2 is zero, it indicates that F2 is parallel or collinear to the X-axis. However, it does not provide information about the direction or the y and z components of F2. Further analysis or information is required to determine these aspects.
A vector F1 is along the positive X axis. If its vector product wiyh a...
F2 is directed along x-axis (it may be both in +ve or in. -ve direction)