Question

For vectors vector(a, b, c) if each vector is perpendicular to the sum of remaining two vectors and |vector a| = 3, |vector b| = 4, |vector c| = 5, then vector|a + b + c| =____

(A) 2√2

(B) 3√2

(C) 4√2

(D) 5√2

Answer 1

The correct option (D) 5√2   

Explanation:

given: |vector a| = 3, |vector b| = 4 and |vector c| = 5

also     vector a ∙ vector(b + c) = 0, vector b ∙ vector(c + a) = 0, vector c ∙ vector(a + b) = 0

∴ 2vector(a ∙ b + b ∙ c + c ∙ a) = 0

Now    vector|a + b + c|²   = |vector a|² + |vector b|² + |vector c|² + 2vector(a ∙ b + b ∙ c + c ∙ a)

= 32 + 42 + 52 + 2(0)

= 50

∴ vector|a + b + c| = 5√2.