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Linear Algebra

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Moderate

Orthogonal vectors and Planes

LINALG-HXFGXL

Suppose that the plane $P$ in $\mathbb{R}^3$ contains the vectors $\mathbf{u} = (1,0,1)$ and $\mathbf{v} = (0,1,1)$.

Which of the following describes $P$?

A

$P$ consists of all vectors orthogonal to $(1,0,1)$ and $(0,1,1)$.

B

$P$ consists of all vectors orthogonal to $\mathbf{u} - \mathbf{v}$

C

$P$ consists of all vectors orthogonal to $\mathbf{u} - 2 \mathbf{v}$

D

$P$ consists of all vectors orthogonal to $(1,1,-1)$

E

$P$ consists of all vectors orthogonal to $(1,0,-1)$