Ortogonaaliprojektio 3-ulotteisesta avaruudesta tasolle


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Picture for Question 1

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Question 1

Why is XX' fixed when you move V11, V12, V21 or V22 (on the lines below the left picture).

Picture for Questions 2

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Questions 2

a) Is it possible for any vector V1 to choose V2 such that the plane spanned by V1,V2 looks like a line (call it L) ?
yes no don't know
b) Does XX' look perpendicular to L ? yes no don't know
c) Is it true for all choises for V1 ? yes no don't know

Picture for Questions 3

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Questions 3

a) Does the property observed in the preceding picture stay valid when you change parameters S1, S2 and/or S3 ?
yes no don't know
b) How does the vector S = (S1,S2,S3) look like on the screen ?

Picture for Questions 4

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Questions 4

a) Compute the matrix of the orthogonal projection on the subspace spanned by S.

b) Compute the matrix P of the orthogonal projection on the plane orthogonal to S.

c) Let i, j, k be an orthonormal basis of the Euclidean 3-space and let S = S1 i + S2 j + S3 k. Compute the lengths of the projections on the orthogonal complement of S, of the vectors i, j, k, j - k, k - i, i - j.

d) Do your results fit with the pictures 2 and 3?
yes no don't know

Question 5: Student feedback and evaluation of problems and pictures



Anyone interested in this kind of worksheets, please contact:
Martti.Pesonen@Joensuu.Fi

Eric Lehman and Martti E. Pesonen, March 23, 2003