Question

The scalar product of the vector i + j + k with a unit vector along the sum of vectors. 2i + 4j - 5k and λi + 2j + 3k is equal to 1. Find the value of λ.

Answer 1

Suppose vector a = 2i + 4j - 5k; vector b = λi + 2j + 3k

Then vector(a + b) = (2 + λ)i + 6j - 2k

Along the unit Vector, sum of these vectors

= 1 x (2 + λ) + 1 x 6 + 1 x (-2) = √((2 + λ)2 + 40)

λ + 6 = √((2 + λ)2 + 40)

λ2 + 12λ + 36 = 4 + 4λ + λ2 + 40

12λ + 36 = 4λ + 44

λ = 1