Let a → and b → are two non-collinear vector such that a → = 1 . The angles of a triangle whose two sides are represented by vectors 3 a → × b → and b → - a → ⋅ b → a → are

Question

Let a → and b → are two non-collinear vector such that a → = 1 . The angles of a triangle whose two sides are represented by vectors 3 a → × b → and b → - a → ⋅ b → a → are, π 2 , π 4 , π 4, π 2 , π 3 , π 6, π 2 , 5 π 12 , π 12, π 4 , π 3 , 5 π 12

MARKS App · Accepted Answer

Let, A → = 3 a → × b → B → = b → - a → ⋅ b → a → A → ⋅ B → = 0 ⇒ A → is perpendicular to B → A → = 3 a → × b → = 3 a → b → sin ⁡ θ = 3 b → sin ⁡ θ B → 2 = b → - a → ⋅ b → a → 2 = b → 2 + a → ⋅ b → 2 a → 2 - 2 a → ⋅ b → 2 = b → 2 + b → 2 cos 2 ⁡ θ - 2 b → 2 cos 2 ⁡ θ = b → 2 sin 2 ⁡ θ ⇒ B → = b → sin ⁡ θ A → B → = 3 1 ⇒ other two angles are π 6 , π 3

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