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How to measure the magnitude or length of a vector??

How to measure the magnitude or length of a vector??

Grade:Upto college level

1 Answers

Deepak Patra
askIITians Faculty 471 Points
12 years ago

The formula for the length OP or |p| is a kind of 3 dimensional form of Pythagoras' theorem.
Here's how the working would go if we had a = 4 and b = 3 and c = 12.
Using Pythagoras' theorem in the yellow right-angled triangle we get 

OQ = the square root of (16 + 9) = 5

and then, using Pythagoras' theorem in the vertical green right-angled triangle, we get
OP = the square root of (25 + 144) = 13.

Alternatively, in just one step of working, we have

OP = the square root of (16 + 9 + 144) = 13.

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