Let u = (1, -2, 2, 0). Find a unit vector of v in the same direction o | Mathematics II 2080.1

Mathematics II2080.15 marksNumerical: unit vector computationInner product, Length, and orthoganility

Let u = (1, -2, 2, 0). Find a unit vector of v in the same direction of u. [5]

Vector: $u = (1, -2, 2, 0)$ $\u\ = \sqrt{u1^2 + u2^2 + u3^2 + u4^2}$ $\u\ = \sqrt{(1)^2 + (-2)^2 + (2)^2 + (0)^2} = \sqrt{1 + 4 + 4 + 0} = \sqrt{9} = 3$ The unit vector in the same direction as $u$ is: $v = \frac{u}{\u\} = \frac{1}{3}(1, -2, 2, 0)$ $$\boxed{v = \left(\tfrac{1}{3},\ -\tfra...

Vector: $u = (1, -2, 2, 0)$ $$\u\ = \sqrt{u1^2 + u2^2 + u3^2 + u4^2}$$ $$\u\ = \sqrt{(1)^2 + (-2)^2 + (2)^2 + (0)^2} = \sqrt{1 + 4 + 4 + 0} = \sqrt{9} = 3$$ The unit vector in the same direction as $u$ is: $$v = \frac{u}{\u} = \frac{1}{3}(1, -2, 2, 0)$$ $$\boxed{v = \left(\tfrac{1}{3},\ -\tfra...