Passage: Let a , b , c be unit vectors. Further, a is perpendicular to b ; c makes an angle 3 with both a and b ; and c =p a +q b +r( a b ) . Question: What is the value of (p+q) ?

Step-by-step solution

Given | a | = | b | = | c | = 1 and a b = 0 . Since c makes an angle 3 with both a and b : c a = | c || a | ( 3 ) = 1 2 c b = | c || b | ( 3 ) = 1 2 We are given the relation: c = p a + q b + r( a b ) Taking the dot product of both sides with a : c a = p( a a ) + q( b a ) + r(( a b ) a ) Since a a = 1 , b a = 0 , and ( a b ) a = 0 , we get: p = 1 2 Taking the dot product of both sides with b : c b = p( a b ) + q( b b ) + r(( a b ) b ) Since b b = 1 , a b = 0 , and ( a b ) b = 0 , we get: q = 1 2 Therefore, p + q =