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2⋅⟨−cos⁡(t)2,0,−sin⁡(t)2⟩2\cdot \left\langle - \frac{\cos{\left(t \right)}}{2}, 0, - \frac{\sin{\left(t \right)}}{2}\right\rangle

The calculator will multiply the vector ⟨−cos⁡(t)2,0,−sin⁡(t)2⟩\left\langle - \frac{\cos{\left(t \right)}}{2}, 0, - \frac{\sin{\left(t \right)}}{2}\right\rangle by the scalar 22, with steps shown.
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Your Input

Calculate 2⋅⟨−cos⁡(t)2,0,−sin⁡(t)2⟩2\cdot \left\langle - \frac{\cos{\left(t \right)}}{2}, 0, - \frac{\sin{\left(t \right)}}{2}\right\rangle.

Solution

Multiply each coordinate of the vector by the scalar:

(2)⋅⟨−cos⁡(t)2,0,−sin⁡(t)2⟩=⟨(2)⋅(−cos⁡(t)2),(2)⋅(0),(2)⋅(−sin⁡(t)2)⟩=⟨−cos⁡(t),0,−sin⁡(t)⟩{\color{DarkMagenta}\left(2\right)}\cdot \left\langle - \frac{\cos{\left(t \right)}}{2}, 0, - \frac{\sin{\left(t \right)}}{2}\right\rangle = \left\langle {\color{DarkMagenta}\left(2\right)}\cdot \left(- \frac{\cos{\left(t \right)}}{2}\right), {\color{DarkMagenta}\left(2\right)}\cdot \left(0\right), {\color{DarkMagenta}\left(2\right)}\cdot \left(- \frac{\sin{\left(t \right)}}{2}\right)\right\rangle = \left\langle - \cos{\left(t \right)}, 0, - \sin{\left(t \right)}\right\rangle

Answer

2⋅⟨−cos⁡(t)2,0,−sin⁡(t)2⟩=⟨−cos⁡(t),0,−sin⁡(t)⟩2\cdot \left\langle - \frac{\cos{\left(t \right)}}{2}, 0, - \frac{\sin{\left(t \right)}}{2}\right\rangle = \left\langle - \cos{\left(t \right)}, 0, - \sin{\left(t \right)}\right\rangleA