Justin's Blog

February 18, 2012

Basis Vector

Normalized Vector

Orthogonal Vectors

There are as many basis vectors as there are dimenions in a coordinate scheme.

Thus: a 3D rectangular scheme (called i$ℝ^{3}i$ for Real, 3 dimensions) has 3 basis vectors, all perpendicular to each other.

You often see i, j, and k used as basis vectors. These usually refer to i$ℝ^{3}i$

You can write them out in vector form. $$\hat{i} = (1, 0, 0)$$ $$\hat{j} = (0, 1, 0)$$ $$\hat{k} = (0,0,1)$$

They are useful because you can describe any point in a coordinate system as a sum of the basis vectors, multiplied by a number.

$$(3, 4, 5)$$

Means the same as... $$3\hat{ i} + 4\hat{j} + 5\hat{k}$$

It can make addition and multiplication conceptually simpler.

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