Let a = i -2 j , b =2 j +3 k , c = pi + q j and d = p j - q k be four vectors. If ( a b ) c =3=( a b ) d , then 3 p + q =

Step-by-step solution

a = i -2 j , b =2 j +3 k , c =p i +q j and d =p j -q k Also, we have ( a b ) c =3=( a b ) d ( a b )= | array ccc i & j & k 1 & -2 & 0 0 & 2 & 3 array | aligned & = i (-6-0)- j (3-0)+ k (2-0) & =-6 i -3 j +2 k & a b =-6 i -3 j +2 k aligned Then, ( a b ) c =(-6 i -3 j +2 k ) (p i +q j ) 3=0-6 p+2 q -6 p-3 q=3 ...(i) and ( a b ) d =(-6 i -3 j +2 k ) (p j -q k )=-3 p-2 q 3=-3 p-2 q ...(ii) Solving eqns. (i) and (ii), we get : p=1 and q=-3 Now, 3 p+q=3 1+(-3)=3-3=0 3 p+q=0