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Let vector A, B, C be vectors of length 3, 4, 5 respectively. Let vector A be perpendicular to vector(B + C), vector B or vector(C + A)

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Let vector A, B, C be vectors of length 3, 4, 5 respectively. Let vector A be perpendicular to vector(B + C), vector B or vector(C + A) and vector C to vector(A + B). Then the length of vector(A + B + C) is ....

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Given,

= 9 + 16 + 25 + 0

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