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Actions with linear operators

Generalized projection operator

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Let $a$ and $b$ be some non-parallel lines going through the origin. Let $\mathcal{A}$ be the projection operator of any plane vector on $a$ , and $\mathcal{B}$ be the projection operator of any plane vector on $b$ .

Non-parallel lines passing through the origin

What is $\mathcal{C} = \mathcal{A}+\mathcal{B}$ ?

Select one option from the list

The symmetry operator with respect to the origin.

The identity operator

The symmetry operator about the line

a

The symmetry operator about the line

b

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