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$$$\frac{1}{\sqrt{9 t^{4} + 4 t^{2} + 49}}\cdot \left\langle 7, 2 t, 3 t^{2}\right\rangle$$$
Your Input
Calculate $$$\frac{1}{\sqrt{9 t^{4} + 4 t^{2} + 49}}\cdot \left\langle 7, 2 t, 3 t^{2}\right\rangle$$$.
Solution
Multiply each coordinate of the vector by the scalar:
$$${\color{SaddleBrown}\left(\frac{1}{\sqrt{9 t^{4} + 4 t^{2} + 49}}\right)}\cdot \left\langle 7, 2 t, 3 t^{2}\right\rangle = \left\langle {\color{SaddleBrown}\left(\frac{1}{\sqrt{9 t^{4} + 4 t^{2} + 49}}\right)}\cdot \left(7\right), {\color{SaddleBrown}\left(\frac{1}{\sqrt{9 t^{4} + 4 t^{2} + 49}}\right)}\cdot \left(2 t\right), {\color{SaddleBrown}\left(\frac{1}{\sqrt{9 t^{4} + 4 t^{2} + 49}}\right)}\cdot \left(3 t^{2}\right)\right\rangle = \left\langle \frac{7}{\sqrt{9 t^{4} + 4 t^{2} + 49}}, \frac{2 t}{\sqrt{9 t^{4} + 4 t^{2} + 49}}, \frac{3 t^{2}}{\sqrt{9 t^{4} + 4 t^{2} + 49}}\right\rangle$$$
Answer
$$$\frac{1}{\sqrt{9 t^{4} + 4 t^{2} + 49}}\cdot \left\langle 7, 2 t, 3 t^{2}\right\rangle = \left\langle \frac{7}{\sqrt{9 t^{4} + 4 t^{2} + 49}}, \frac{2 t}{\sqrt{9 t^{4} + 4 t^{2} + 49}}, \frac{3 t^{2}}{\sqrt{9 t^{4} + 4 t^{2} + 49}}\right\rangle = \left\langle \frac{7}{\left(9 t^{4} + 4 t^{2} + 49\right)^{0.5}}, \frac{2 t}{\left(9 t^{4} + 4 t^{2} + 49\right)^{0.5}}, \frac{3 t^{2}}{\left(9 t^{4} + 4 t^{2} + 49\right)^{0.5}}\right\rangle$$$A