If v= (2, 4, 4) and ‖ k v ‖ = 24, then the value of k is:

Question

If v= (2, 4, 4) and ‖ k v ‖ = 24, then the value of k is:

Answer 1

<kv, kv> = 24² = 576 (i.e., if you take dot product of a vector with itself, result is the norm squared.)

On the other hand, <kv, kv> = k²<v, v> = k²(2² + 4² + 4²) = 36k².

Therefore k² = 576/36 = 16. So k = ±4