Let u and v be two vectors. Then, u - v = | u - v | if and only if

Question

Let u and v be two vectors. Then, u - v = | u - v | if and only if, u = v, u and v have the opposite direction, u and v have the same direction, u and v are perpendicular to each other

MARKS App · Accepted Answer

Let u and v be two vector ⇒ u - v = u - v (Given) ⇒ ( u - v ) 2 = ( u - v ) 2 ⇒ u 2 + v 2 - 2 u v = u 2 + v 2 - 2 u v cos θ ⇒ cos θ = 1 ⇒ θ = 0 , 2 π ⇒ u and v have the same direction.

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