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53434⋅⟨1,−1225,925⟩\frac{5 \sqrt{34}}{34}\cdot \left\langle 1, - \frac{12}{25}, \frac{9}{25}\right\rangle

The calculator will multiply the vector ⟨1,−1225,925⟩\left\langle 1, - \frac{12}{25}, \frac{9}{25}\right\rangle by the scalar 53434\frac{5 \sqrt{34}}{34}, with steps shown.
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Your Input

Calculate 53434⋅⟨1,−1225,925⟩\frac{5 \sqrt{34}}{34}\cdot \left\langle 1, - \frac{12}{25}, \frac{9}{25}\right\rangle.

Solution

Multiply each coordinate of the vector by the scalar:

(53434)⋅⟨1,−1225,925⟩=⟨(53434)⋅(1),(53434)⋅(−1225),(53434)⋅(925)⟩=⟨53434,−63485,934170⟩{\color{Purple}\left(\frac{5 \sqrt{34}}{34}\right)}\cdot \left\langle 1, - \frac{12}{25}, \frac{9}{25}\right\rangle = \left\langle {\color{Purple}\left(\frac{5 \sqrt{34}}{34}\right)}\cdot \left(1\right), {\color{Purple}\left(\frac{5 \sqrt{34}}{34}\right)}\cdot \left(- \frac{12}{25}\right), {\color{Purple}\left(\frac{5 \sqrt{34}}{34}\right)}\cdot \left(\frac{9}{25}\right)\right\rangle = \left\langle \frac{5 \sqrt{34}}{34}, - \frac{6 \sqrt{34}}{85}, \frac{9 \sqrt{34}}{170}\right\rangle

Answer

53434⋅⟨1,−1225,925⟩=⟨53434,−63485,934170⟩≈⟨0.857492925712544,−0.411596604342021,0.308697453256516⟩\frac{5 \sqrt{34}}{34}\cdot \left\langle 1, - \frac{12}{25}, \frac{9}{25}\right\rangle = \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\rangleA