Question

Q. A vector A in OX1X2X3 has components (2, 1, -2). Find its components in OX1’X2’X3’. The transformation between the coordinates X1, X2, X3 and X1’ , X2’ , X3’ is defined by
X1’=1/3 (2x1+2x2-x3)
X2’=1/3 (2x1-x2+2x3)
X3’=1/3(-x1+2x2+2x3)

Answer 1

Answer on Question #64382 – Math – Linear Algebra

Question

A vector A in OX1X2X3 has components (2, 1, -2). Find its components in OX1'X2'X3'. The transformation between the coordinates X1, X2, X3 and X1', X2', X3' is defined by

$$X1' = 1/3 (2x1 + 2x2 - x3)$$ $$X2' = 1/3 (2x1 - x2 + 2x3)$$ $$X3' = 1/3(-x1 + 2x2 + 2x3)$$

Solution

Components of vector A in OX1' X2' X3' are as follows:

$$X1' = 1/3(2*2 + 2*1 - (-2)) = 1/3(4 + 2 + 2) = 8/3,$$ $$X2' = 1/3(2*2 - 1 + 2(-2)) = 1/3(4 - 1 - 4) = -1/3,$$ $$X3' = 1/3(-2 + 2*1 + 2(-2)) = 1/3(-2 + 2 - 4) = -4/3.$$

Answer: 8/3, -1/3, -4/3.

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