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Three vectors →a, →b and →c have magnitudes |→a| = 4, |→b| = 4 and |→c| = 2. If →a is orthogonal to (→b + →c), →b is orthogonal to (→c + →a), and →c is orthogonal to (→a + →b), then the magnitude of (→a + →b + →c) is:

1. 9
2. 6
3. 5
4. 4

Correct answer: 6

Solution

Adding a.(b+c)=0, b.(c+a)=0, c.(a+b)=0 gives 2(a.b+b.c+c.a)=0. Then |a+b+c|^2 = 16+16+4+0 = 36, so the magnitude is 6.

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