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$$$\frac{e^{- 2 t}}{2}\cdot \left\langle 2 e^{2 t}, 0\right\rangle$$$

The calculator will multiply the vector $$$\left\langle 2 e^{2 t}, 0\right\rangle$$$ by the scalar $$$\frac{e^{- 2 t}}{2}$$$, with steps shown.
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Your Input

Calculate $$$\frac{e^{- 2 t}}{2}\cdot \left\langle 2 e^{2 t}, 0\right\rangle$$$.

Solution

Multiply each coordinate of the vector by the scalar:

$$${\color{Magenta}\left(\frac{e^{- 2 t}}{2}\right)}\cdot \left\langle 2 e^{2 t}, 0\right\rangle = \left\langle {\color{Magenta}\left(\frac{e^{- 2 t}}{2}\right)}\cdot \left(2 e^{2 t}\right), {\color{Magenta}\left(\frac{e^{- 2 t}}{2}\right)}\cdot \left(0\right)\right\rangle = \left\langle 1, 0\right\rangle$$$

Answer

$$$\frac{e^{- 2 t}}{2}\cdot \left\langle 2 e^{2 t}, 0\right\rangle = \left\langle 1, 0\right\rangle$$$A