perpendicular vectors

**Haris** · November 25th 2008, 12:20 AM

Let

and let

. Find vectors

such that

with

parallel to

and

perpendicular to

.

Any help with this question would be brilliant cheers x

**Opalg** · November 25th 2008, 02:59 AM

Originally Posted by Haris

Let

and let

. Find vectors

such that

with

parallel to

and

perpendicular to

.

The formula for a is $\mathbf{a} = (\mathbf{v.u}/\|\mathbf{u}\|^2)\mathbf{u}$ , where the dot denotes the scalar product and $\|\mathbf{u}\| = (4^2+(-4)^2+5^2)^{1/2}$ is the norm (or length) of u. Once you have found a, let b=v-a, and keep your fingers crossed that b is orthogonal (perpendicular) to u.

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