Gunsaz

2022-10-08

Write the set of vectors that are orthogonal to v as a linear combination of two unit vectors.

$v=\u27e81,-\sqrt{8},-\sqrt{8}\u27e9\text{is a vector.}$ is a vector.

I know I have to find two unit vectors u and w so that any vector that is orthogonal to v can be expressed as a linear combination of u and w.

Help, please.

$v=\u27e81,-\sqrt{8},-\sqrt{8}\u27e9\text{is a vector.}$ is a vector.

I know I have to find two unit vectors u and w so that any vector that is orthogonal to v can be expressed as a linear combination of u and w.

Help, please.

xgirlrogueim

Beginner2022-10-09Added 13 answers

Make an ansatz $u=\u27e8x,y,0\u27e9$ and from $v\perp u$ and $\Vert u\Vert =1$ obtain conditions for x,y. After that, do the same with $w=\u27e80,y,z\u27e9$

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