Say you have 2 displacement vectors lining up to form a right angle, one being 4m and the other being 3m. You can add these 2 vectors to get another vector that has a magnitude of 7m, forming a hypotenuse to make a triangle. You can also find the magnitude of a vector by using the Pythagorean Theorem, so 3^2 + 4^2 = x^2. x=5. This says that the magnitude of the vector found by the Pythagorean method is 5m, which does not agree with the previous measurement of 7m. Could someone please explain why this is so?
-
You can't just add the lengths of the vectors. The calculation by the Pythagorean Theorem is correct.
Use north and east as your directions. If you walk 4m north and then 3m east, then although you have walked 7m around the outside of the triangle, your distance from the start is only 5m.
If the vectors are in a straight line, their sum has magnitude of 7m.
If the vectors are at a right angle, their sum has magnitude of 5m.
If the vectors are facing in opposite directions, their sum has magnitude of 1m.
Use north and east as your directions. If you walk 4m north and then 3m east, then although you have walked 7m around the outside of the triangle, your distance from the start is only 5m.
If the vectors are in a straight line, their sum has magnitude of 7m.
If the vectors are at a right angle, their sum has magnitude of 5m.
If the vectors are facing in opposite directions, their sum has magnitude of 1m.
-
The only way you could get 7 would be if you put the 3 and 4 magnitude vectors end to end. Something doesn't make sense....