Question

Find the value of the constant S such that the scalar product of the vector (i + j + k) with the unit vector parallel to the sum of the vectors (2i + 4j – 5k) and (Si + 2j + 3k) is equal to 1. 

Answer 1

Sum of the vectors

= (2i + 4j – 5k) + (Si + 2j + 3k)

= (2 + S)i + 6j – 2k

Unit vector parallel to the sum of the vectors

(2 + S) + 6 – 2 = √(S² + 36 + 44)

(S + 6)² = (S² + 4S + 44)

S² + 12S + 36 = (S² + 4S + 44)

8S = 8

S = 1