Español | Português
  1. Home
  2. Calculators
  3. Calculators: Linear Algebra
  4. Linear Algebra Calculator

$$$\frac{4}{\sqrt{26 - 26 \cos{\left(4 t \right)}}}\cdot \left\langle 3 \sin^{2}{\left(t \right)} \cos{\left(t \right)}, - 3 \sin{\left(t \right)} \cos^{2}{\left(t \right)}, \sin{\left(2 t \right)}\right\rangle$$$

The calculator will multiply the vector $$$\left\langle 3 \sin^{2}{\left(t \right)} \cos{\left(t \right)}, - 3 \sin{\left(t \right)} \cos^{2}{\left(t \right)}, \sin{\left(2 t \right)}\right\rangle$$$ by the scalar $$$\frac{4}{\sqrt{26 - 26 \cos{\left(4 t \right)}}}$$$, with steps shown.
$$$\langle$$$ $$$\rangle$$$
Comma-separated.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Your Input

Calculate $$$\frac{4}{\sqrt{26 - 26 \cos{\left(4 t \right)}}}\cdot \left\langle 3 \sin^{2}{\left(t \right)} \cos{\left(t \right)}, - 3 \sin{\left(t \right)} \cos^{2}{\left(t \right)}, \sin{\left(2 t \right)}\right\rangle.$$$

Solution

Multiply each coordinate of the vector by the scalar:

$$${\color{BlueViolet}\left(\frac{4}{\sqrt{26 - 26 \cos{\left(4 t \right)}}}\right)}\cdot \left\langle 3 \sin^{2}{\left(t \right)} \cos{\left(t \right)}, - 3 \sin{\left(t \right)} \cos^{2}{\left(t \right)}, \sin{\left(2 t \right)}\right\rangle = \left\langle {\color{BlueViolet}\left(\frac{4}{\sqrt{26 - 26 \cos{\left(4 t \right)}}}\right)}\cdot \left(3 \sin^{2}{\left(t \right)} \cos{\left(t \right)}\right), {\color{BlueViolet}\left(\frac{4}{\sqrt{26 - 26 \cos{\left(4 t \right)}}}\right)}\cdot \left(- 3 \sin{\left(t \right)} \cos^{2}{\left(t \right)}\right), {\color{BlueViolet}\left(\frac{4}{\sqrt{26 - 26 \cos{\left(4 t \right)}}}\right)}\cdot \left(\sin{\left(2 t \right)}\right)\right\rangle = \left\langle \frac{6 \sqrt{26} \sin^{2}{\left(t \right)} \cos{\left(t \right)}}{13 \sqrt{1 - \cos{\left(4 t \right)}}}, - \frac{6 \sqrt{26} \sin{\left(t \right)} \cos^{2}{\left(t \right)}}{13 \sqrt{1 - \cos{\left(4 t \right)}}}, \frac{2 \sqrt{26} \sin{\left(2 t \right)}}{13 \sqrt{1 - \cos{\left(4 t \right)}}}\right\rangle$$$

Answer

$$$\frac{4}{\sqrt{26 - 26 \cos{\left(4 t \right)}}}\cdot \left\langle 3 \sin^{2}{\left(t \right)} \cos{\left(t \right)}, - 3 \sin{\left(t \right)} \cos^{2}{\left(t \right)}, \sin{\left(2 t \right)}\right\rangle = \left\langle \frac{6 \sqrt{26} \sin^{2}{\left(t \right)} \cos{\left(t \right)}}{13 \sqrt{1 - \cos{\left(4 t \right)}}}, - \frac{6 \sqrt{26} \sin{\left(t \right)} \cos^{2}{\left(t \right)}}{13 \sqrt{1 - \cos{\left(4 t \right)}}}, \frac{2 \sqrt{26} \sin{\left(2 t \right)}}{13 \sqrt{1 - \cos{\left(4 t \right)}}}\right\rangle\approx \left\langle \frac{2.353393621658208 \sin^{2}{\left(t \right)} \cos{\left(t \right)}}{\left(1 - \cos{\left(4 t \right)}\right)^{0.5}}, - \frac{2.353393621658208 \sin{\left(t \right)} \cos^{2}{\left(t \right)}}{\left(1 - \cos{\left(4 t \right)}\right)^{0.5}}, \frac{0.784464540552736 \sin{\left(2 t \right)}}{\left(1 - \cos{\left(4 t \right)}\right)^{0.5}}\right\rangle$$$A