As u = (2, -2, 3) and v = (1, -3, 4), then ||-2u + 2v|| is ______?

2√3

√2

√3

None of these

Calculation: First, compute -2u + 2v:−2u=(−4,4,−6)−2u=(−4,4,−6)2v=(2,−6,8)2v=(2,−6,8)−2u+2v=(−4+2,4−6,−6+8)=(−2,−2,2)−2u+2v=(−4+2,4−6,−6+8)=(−2,−2,2)

Calculation: First, compute -2u + 2v:
- $- 2 u = (- 4, 4, - 6)$
- $2 v = (2, - 6, 8)$
- $- 2 u + 2 v = (- 4 + 2, 4 - 6, - 6 + 8) = (- 2, - 2, 2)$
Norm Calculation: The norm (magnitude) of $- 2 u + 2 v$ is:
$∣ ∣ - 2 u + 2 v ∣ ∣ = \sqrt{(- 2)^{2} + (- 2)^{2} + 2^{2}} = \sqrt{4 + 4 + 4} = \sqrt{12} = 2 \sqrt{3}$

Answer: