The vectors, (2, -1) and (4, 8), are
1)parallel
2)perpendicular
3)neither parallel or perpendicular
Well, let's see if we can solve this puzzler with a little bit of humor!
Hmm, comparing these two vectors, it seems like they're on very different paths. The first vector, (2, -1), is like a lost puppy wandering in one direction, while the second vector, (4, 8), is like a rocket zooming off in another direction.
So, based on their different paths, I'd say these vectors are neither parallel nor perpendicular. They're just going their separate ways, like two ships passing in the night.
Hope that brought a smile to your face!
To determine if two vectors are parallel, we need to check if they have the same direction. To determine if two vectors are perpendicular, we need to check if their dot product is zero.
Let's calculate the dot product of the given vectors:
(2, -1) dot (4, 8) = (2 * 4) + (-1 * 8) = 8 - 8 = 0
Since the dot product is zero, we can conclude that the vectors are perpendicular to each other.
To determine if two vectors are parallel or perpendicular, we need to compare their slopes. The slopes of the vectors can be found by dividing the y-component by the x-component.
Let's find the slopes of the given vectors:
Vector (2, -1):
Slope = (-1) / 2 = -1/2
Vector (4, 8):
Slope = 8 / 4 = 2
Now, let's analyze the slopes:
1) If the slopes of the two vectors are equal, then they are parallel.
2) If the product of the slopes is -1, then the vectors are perpendicular.
3) If neither of the above conditions is satisfied, then the vectors are neither parallel nor perpendicular.
Comparing the calculated slopes:
- The slope of vector (2, -1) is -1/2.
- The slope of vector (4, 8) is 2.
Since the slopes are not equal and their product is not -1, we can conclude that the vectors (2, -1) and (4, 8) are neither parallel nor perpendicular to each other.
Therefore, the answer is 3) neither parallel nor perpendicular.