Find a unit vector v of u = (1, -2, 2, 3) in the direction of u. | Mathematics II 2078

Mathematics II20785 marksNumerical: unit vector directionInner product, Length, and orthoganility

Find a unit vector $v$ of $u = (1, -2, 2, 3)$ in the direction of $u$ . [5]

Find a unit vector $v$ of $u = (1, -2, 2, 3)$ in the direction of $u$. [5]

$u = (1,\ -2,\ 2,\ 3)$ The unit vector in the direction of $u$ is: $\hat{u} = \frac{u}{\u\}, \qquad \u\ = \sqrt{u1^2 + u2^2 + u3^2 + u4^2}$ $\u\ = \sqrt{(1)^2 + (-2)^2 + (2)^2 + (3)^2} = \sqrt{1 + 4 + 4 + 9} = \sqrt{18} = 3\sqrt{2}$ $$\hat{u} = \frac{1}{3\sqrt{2}}(1,\ -2,\ 2,\ 3) = \left(\f...

$$u = (1,\ -2,\ 2,\ 3)$$ The unit vector in the direction of $u$ is: $$\hat{u} = \frac{u}{\u}, \qquad \u\ = \sqrt{u1^2 + u2^2 + u3^2 + u4^2}$$ $$\u\ = \sqrt{(1)^2 + (-2)^2 + (2)^2 + (3)^2} = \sqrt{1 + 4 + 4 + 9} = \sqrt{18} = 3\sqrt{2}$$ $$\hat{u} = \frac{1}{3\sqrt{2}}(1,\ -2,\ 2,\ 3) = \left(\f...

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