If a = m b + n c , where a =4 i +13 j -18 k , b = i -2 j +3 k , c =2 i +3 j -4 k , then m + n =

Step-by-step solution

Given: aligned & a =4 i +13 j -18 k & b = i -2 j +3 k & c =2 i +3 j -4 k aligned Also, a =m b +n c aligned & 4 i +13 j -18 k =m( i -2 j +3 k )+n(2 i +3 j -4 k ) & 4 i +13 j -18 k & =(m+2 n) i +(-2 m+3 n) j +(3 m-4 n) k aligned Comparing, we get m+2 n=4 and -2 m+3 n=13 Solving above equations, we get aligned & m =-2 and n =3 & m + n =-2+3=1 aligned