If a unit vector a → makes angles π 3 with i ^ , π 4 with j ^ and θ ∈ 0 , π with k ^ , then a value of θ is:

Step-by-step solution

The unit vector a → makes angle π 3 ,   π 4 and θ with i ^ ,   j ^   &   k ^ respectively. Hence, the direction cosines of the vector a → are cos α = cos π 3 = 1 2 ,   cos β = cos π 4 = 1 2 and cos γ = cos θ For a line having direction cosines as cos α ,   cos β ,   cos γ ⇒ c o s 2 α + c o s 2 β + c o s 2 γ = 1 ⇒ 1 4 + 1 2 + c o s 2 θ = 1 ⇒ c o s 2 θ = 1 - 3 4 = 1