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Unit vector in the direction of ⟨2cos⁡(t),−2sin⁡(t),0⟩\left\langle 2 \cos{\left(t \right)}, - 2 \sin{\left(t \right)}, 0\right\rangle

The calculator will find the unit vector in the direction of the vector ⟨2cos⁡(t),−2sin⁡(t),0⟩\left\langle 2 \cos{\left(t \right)}, - 2 \sin{\left(t \right)}, 0\right\rangle, with steps shown.
⟨\langle ⟩\rangle
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Your Input

Find the unit vector in the direction of u⃗=⟨2cos⁡(t),−2sin⁡(t),0⟩\mathbf{\vec{u}} = \left\langle 2 \cos{\left(t \right)}, - 2 \sin{\left(t \right)}, 0\right\rangle.

Solution

The magnitude of the vector is ∣u⃗∣=2\mathbf{\left\lvert\vec{u}\right\rvert} = 2 (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 e⃗=⟨cos⁡(t),−sin⁡(t),0⟩\mathbf{\vec{e}} = \left\langle \cos{\left(t \right)}, - \sin{\left(t \right)}, 0\right\rangle (for steps, see vector scalar multiplication calculator).

Answer

The unit vector in the direction of ⟨2cos⁡(t),−2sin⁡(t),0⟩\left\langle 2 \cos{\left(t \right)}, - 2 \sin{\left(t \right)}, 0\right\rangleA is ⟨cos⁡(t),−sin⁡(t),0⟩\left\langle \cos{\left(t \right)}, - \sin{\left(t \right)}, 0\right\rangleA.