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(i) If vector a = i + 2j - 3k and vector b = 3i - j + 2k, show that vector (a + b) is perpendicular to vector (a - b).

(ii) If vector a = (5i - j - k) and vector b = (i + 3j - 5k) then show that vector (a + b) and vector (a - b) are orthogonal.

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(i) It is given that

So we get

= (4 x -2) + (1 x 3) + (-1 x -5)

= -8 + 3 + 5

= 0

Hence, it is proved that the vector(a + b) is perpendicular to vector (a - b)

(ii) It is given that

= 24 - 8 - 16

= 0 

Here the dot product of vector(a + b) and vector(a - b) is zero.

Hence, it is proved that the vector(a + b) is orthogonal to vector (a - b)

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