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22⋅⟨1,1⟩\frac{\sqrt{2}}{2}\cdot \left\langle 1, 1\right\rangle

The calculator will multiply the vector ⟨1,1⟩\left\langle 1, 1\right\rangle by the scalar 22\frac{\sqrt{2}}{2}, with steps shown.
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Your Input

Calculate 22⋅⟨1,1⟩\frac{\sqrt{2}}{2}\cdot \left\langle 1, 1\right\rangle.

Solution

Multiply each coordinate of the vector by the scalar:

(22)⋅⟨1,1⟩=⟨(22)⋅(1),(22)⋅(1)⟩=⟨22,22⟩{\color{Blue}\left(\frac{\sqrt{2}}{2}\right)}\cdot \left\langle 1, 1\right\rangle = \left\langle {\color{Blue}\left(\frac{\sqrt{2}}{2}\right)}\cdot \left(1\right), {\color{Blue}\left(\frac{\sqrt{2}}{2}\right)}\cdot \left(1\right)\right\rangle = \left\langle \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right\rangle

Answer

22⋅⟨1,1⟩=⟨22,22⟩≈⟨0.707106781186548,0.707106781186548⟩\frac{\sqrt{2}}{2}\cdot \left\langle 1, 1\right\rangle = \left\langle \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right\rangle\approx \left\langle 0.707106781186548, 0.707106781186548\right\rangleA