If the angles between the vectors a → and b → , b → and c → , c → and a → be π 4 , π 3 , π 3 respectively, then the angle which a → makes with the plane containing b → and c → is

Question

If the angles between the vectors a → and b → , b → and c → , c → and a → be π 4 , π 3 , π 3 respectively, then the angle which a → makes with the plane containing b → and c → is, sin - 1 ⁡ 2 3, sin - 1 ⁡ 2 3, sin - 1 ⁡ 1 4, sin - 1 ⁡ 2 3

MARKS App · Accepted Answer

A normal vector perpendicular to the plane is b → × c → sin ⁡ θ = a → ⋅ b → × c → a → b → × c → = a → b → c → a → b → × c → … i b → × c → = b → c → sin ⁡ π 3 = 3 2 b → c → … i i a → b → c → 2 = a → ⋅ a → a → ⋅ b → a → ⋅ c → b → ⋅ a → b → ⋅ b → b → ⋅ c → c → ⋅ a → c → ⋅ b → c → ⋅ c → = a → 2 a → b → 2 a → c → 2 a → b → 2 b → 2 b → c → 2 a → c → 2 b → c → 2 c → 2 = a 2 3 4 b → 2 c → 2 - a → b → 2 a → b → c → 2 1 2 - 1 4 + a → c → 2 a → b → 2 c → 1 2 2 - 1 2 = 1 2 2 a → 2 b → 2 c → 2 ⇒ a → b → c → = 1 2 2 a → b → c → … i i i From i , i i and i i i sin ⁡ θ = 1 2 2 3 2 = 2 3 ⇒ θ = sin - 1 ⁡ 2 3

Search any question & find its solution

Looking for more such questions to practice?