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What is the unit vector that is orthogonal to the plane containing # (-i + j + k) # and # ( i - j + k) #?

Answer 1

Elena Albarran

pl, find the unit vector of the cross product of the given vectors in order

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Answer 2

Layla Ahmed

The unit vector orthogonal to the plane containing (-i + j + k) and (i - j + k) is given by the cross product of the two given vectors, divided by its magnitude. The cross product of the vectors (-i + j + k) and (i - j + k) is (2i + 2j + 2k), and the magnitude of this vector is sqrt(2^2 + 2^2 + 2^2) = sqrt(12) = 2sqrt(3). Therefore, the unit vector orthogonal to the plane containing (-i + j + k) and (i - j + k) is (2i + 2j + 2k) / (2sqrt(3)), which simplifies to (1/sqrt(3)) * (i + j + k).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.