Vector addition

[Ihavesomanyquestions]

I am a little confused about vector addition. In a EK question they stated that a ballon travel up 6 km, north 10 km, and 8 km east. The answer was the square root of the sum of each term squared. Probably simple for most but: R=(36+64+100)^1/2. I was not able to do this problem after the reading. I know that putting vectors head to tail means addition but why they square each term and then take the square root is confusing me. I know the pythagorean theorem. Is it always the case that when the vectors are all perpendicular to one another the resultant vector is the square root of the sum of each term squared?

For example, a man traveled 8 km east, 7 km north, 8 km east, and the 7 km north. Is his final displacement R=(64+49+64+49)^1/2?

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[studyq]

pythagorean theorem applies in 3 planes as well, in other words if something has distance in x, y, and z planes the resultant vector has magnitude sqrt(x^2+y^2+z^2).

your example is incorrect because you need to take the resultant vector in each of the planes. It would be sqrt(14^2+16^2). Because saying 8km east + 8 km east really means 16 km east. (Similar to if you said 8km east and 3km west it would be 5 km east). The example in EK has distance in x, y, and z, (up, north, east).