Question

A and b are 2 vectors such that their resultant vector is perpendicular to a and in magnitude equal to a find the magnitude of vector b

Answer 1

(A+B).A=0         (Since they are perpendicular or cos90° = 0)

|A|² + B.A = 0

⇒ B.A = -|A|²

⇒ |A + B| = |A|

⇒|A|² + |B|² + 2A.B = |A|²

⇒|A|² + |B|²- 2|A|² = |A|²

⇒|B|² = 2|A|²

⇒|B| = √2|A|