Unit vector in the direction of ⟨1, -12/25, 9/25⟩

The calculator will find the unit vector in the direction of the vector

\left\langle 1, - \frac{12}{25}, \frac{9}{25}\right\rangle

, with steps shown.

Your Input

Find the unit vector in the direction of $\mathbf{\vec{u}} = \left\langle 1, - \frac{12}{25}, \frac{9}{25}\right\rangle$ .

Solution

The magnitude of the vector is $\mathbf{\left\lvert\vec{u}\right\rvert} = \frac{\sqrt{34}}{5}$ (for steps, see magnitude calculator).

The unit vector is obtained by dividing each coordinate of the given vector by the magnitude.

Thus, the unit vector is $\mathbf{\vec{e}} = \left\langle \frac{5 \sqrt{34}}{34}, - \frac{6 \sqrt{34}}{85}, \frac{9 \sqrt{34}}{170}\right\rangle$ (for steps, see vector scalar multiplication calculator).

Answer

The unit vector in the direction of $\left\langle 1, - \frac{12}{25}, \frac{9}{25}\right\rangle$ A is $\left\langle \frac{5 \sqrt{34}}{34}, - \frac{6 \sqrt{34}}{85}, \frac{9 \sqrt{34}}{170}\right\rangle\approx \left\langle 0.857492925712544, -0.411596604342021, 0.308697453256516\right\rangle.$ A

Unit vector in the direction of ⟨1,−1225,925⟩\left\langle 1, - \frac{12}{25}, \frac{9}{25}\right\rangle⟨1,−2512​,259​⟩

Your Input

Solution

Answer

Unit vector in the direction of $\left\langle 1, - \frac{12}{25}, \frac{9}{25}\right\rangle$