If a → and b → are two vectors such that a → + b → . a → - b → = 0 , find the relation between the magnitudes of a → and b → .

Given that, a → + b → · a → - b → = 0 ⇒ a → · a → - a → · b → + b → · a → - b → · b → = 0 ⇒ a → 2 - b → 2 = 0 a → · b → = b → · a → ⇒ a → 2 = b → 2 ∴ a → = b → It shows that the magnitude of a → and b → are equal.

For any two vectors a → and b → write when a → + b → = a → + b → holds.

Given that a → + b → = a → + b → Squaring both sides, we get a → + b → 2 = a → + b → 2 ⇒ a → + b → · a → + b → = a → + b → 2 ⇒ a → · a → + a → · b → + b → · a → + b → · b → = a → + b → 2 ⇒ a → 2 + b → 2 + 2 a → · b → = a → 2 + b → 2 + 2 a → b → ⇒ a → · b → = a → b → ⇒ a → b → cos θ = a → b → .............. where θ is the angle between a → and b → ⇒ cos θ = 1 ⇒ θ = 0 ° ⇒ a → and b → are parallel

For any two vectors a → and b → write when a → + b → = a → - b → holds.

Given that a → + b → = a → - b → Squaring both sides, we get a → + b → 2 = a → - b → 2 ⇒ a → + b → · a → + b → = a → - b → · a → - b → ⇒ a → · a → + a → · b → + b → · a → + b → · b → = a → · a → - a → · b → - b → · a → + b → · b → ⇒ a → 2 + b → 2 + 2 a → · b → = a → 2 + b → 2 - 2 a → · b → ⇒ 4 a → · b → = 0 ⇒ a → · b → = 0 ⇒ a → and b → are perpendicular

If a → · a → = 0 and a → · b → = 0 , what can you conclude about the vector b →

Given that a → · a → = 0 ⇒ a → a → cos 0 = 0 ⇒ a → 2 = 0 ⇒ a → = 0 . . . . . 1 Also, given that a → · b → = 0 ⇒ a → b → cos θ = 0 ...........where θ is the angle between a → and b → ⇒ 0 b → cos θ = 0 ............ from ( 1 ) ⇒ 0 = 0 So, it means that for any vector b → , the given equation a → · b → = 0 is satisfied.