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

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

Solution

Let u and v be two vector

⇒u-v=u-v (Given)

⇒(u-v)2=(u-v)2

⇒u2+v2-2uv=u2+v2-2uv cosθ

⇒cosθ=1

⇒θ=0, 2π

⇒  u and v have the same direction.

Asked in: AP EAMCET 2020 (23 Sep Shift 1)

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