The magnitude of the vector product of the vector i + j + k with a unit vector along the sum of vectors 2i + 4j - 5k

Question

The magnitude of the vector product of the vector \(\hat{i}+\hat{j}+\hat{k}\) with a unit vector along the sum of vectors \(2\hat{i}+4\hat{j}-5\hat{k}\) and \(\lambda\hat{i}+2\hat{j}+3\hat{k}\) is equal to \(\sqrt{2}.\) Find the value of λ.

Answer 1

From question

Putting it in (i), we get

Squaring both sides, we get