# linear algebra

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Solve for x if the vectors (2, x, 7-x) and (x, 3, -2) are orthogonal

• linear algebra -

if orthogonal, then their dot product is zero

(2,x,7-x) . (x , 3, -2) = 0
2x + 3x - 14 + 2x = 0
7x = 14
x = 2

check:
(2,2,5).(2,3,-2) = 4 + 6 - 10 = 0

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