Let a = i +3 j - k , b =3 i - j + k and c = i +2 j -2 k where , R , be three vectors. If the projection of a on c is 10 3 and b c =-6 i +10 j +7 k , then the value of ( + ) is equal to

Step-by-step solution

Given vectors a = i +3 j - k , b =3 i - j + k , and c = i +2 j -2 k . The projection of a on c is a c | c | = + 8 3 , since a c = + 6 + 2 and | c | = 3 . Given this equals 10 3 , we find = 2 . Computing b c yields (2 - 2 ) i + (6 + ) j + 7 k . Setting this equal to -6 i + 10 j + 7 k and comparing coefficients gives = 4 . Therefore, + = 2 + 4 = 6 . 6