If a and b are vectors such that | a + b |= 29 and a (2 i +3 j +4 k )=(2 i +3 j +4 k ) b , then a possible value of ( a + b ) (-7 i +2 j +3 k ) is

Step-by-step solution

aligned & a (2 i +3 j +4 k )=(2 i +3 j +4 k ) b =- b (2 i +3 j +4 k ) & ( a + b ) (2 i +3 j +4 k )= 0 & ( a + b ) | 2 i +3 j +4 k & a + b = (2 i +3 j +4 k ) & | a + b |= 2^2+3^2+4^2 & 29 = 29 & = 1 & a + b = (2 i +3 j +4 k ) & ( a + b ) (-7 i +2 j +3 k )= (2 i +3 j +4 k ) (-7 i +2 j +3 k ) & = (-14+6+12) & = 4 aligned