Vectors

In 2D the length of vectors is generally calculated using our Pythagorean Theorem. Here comes the question that how the idea of length of vectors in n-dimensional space i.e is generalised. Or in simpler words how the length of vectors in n-dimensional space comes out to be:-

If provided with some sort of explanation then pls do explain in a detailed way.

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
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Comments

@Pranshu Gaba

Mahrishi Tiwari - 3 years, 2 months ago

@ Rajdeep Dhingra

Mahrishi Tiwari - 3 years, 2 months ago

The "length" is the square root of the Euclidean scalar product.

A Former Brilliant Member - 2 years, 9 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$