Answered

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explain why two lines through the origin that meet at a right angle can be considered orthogonal subspaces of r2 but two planes through the origin that meet at a right angle can not be considered orthogonal subspaces of r3.

Sagot :

There is a difference between orthogonal and orthogonal subspaces. According to this, two planes cannot be orthogonal in R3.

Considering, in the case of the orthogonal planes, each plane should have a basis of orthogonal vectors, and also, one of the pairs in each of the vector,  is shared between the two planes and the other vector that is present, should form a orthogonal pair to each other.

Taking the case of orthogonal subspaces,  the main requirement is that each vector of each of the pairs should be orthogonal to each vector of each of the other pair. Also, the dimension of the ambient pair should be not less than 4 (2+2).

When we talk about two planes in R3, planes are orthogonal if and only if, their normal vectors are orthogonal. If this condition is not present, then planes are not orthogonal in R3.

To know more about orthogonal planes: https://brainly.com/question/29580789

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