This question already has an answer here:
I understand the PCA method in a following way:
0) I have a cloud of dots in ND space
1) I should find a vector which gives me a maximal variance when dots are projected on this vector.
2) I should find the second vector orthogonal to the first, which will explain the maximal possible variance.
And so on..
My question is - if I would use the plane, defined by first and second principal components, will it be the plane, which explains the maximum possible variance?