Question

HELP PLS>>> The vector (3, - 7) ) is rotated by an angle of (3pi)/4 radians and then reflected across the y-axis. If the resulting vector is [a/b], then a=__ and b=__

Answer 1

Answer:

$a \approx -2.826$, $b \approx 7.072$

Step-by-step explanation:

First, the vector must be transformed into its polar form:

$r = \sqrt{3^{2}+ (-7)^{2}}$

$r \approx 7.616$

$\theta \approx 2\pi - \tan^{-1}\left(\frac{7}{3} \right)$

$\theta \approx 1.629\pi$

Let assume that vector is rotated counterclockwise. The new angle is:

$\theta' = \theta + \frac{3\pi}{4}$

$\theta' = 2.379\pi$

Which is coterminal with $\theta'' = 0.379\pi$. The reflection across y-axis is:

$\theta''' = \pi - \theta''$

$\theta''' = 0.621\pi$

The equivalent vector in rectangular coordinates is:

$a = 7.616\cdot \cos 0.621\pi$

$a \approx -2.826$

$b = 7.616\cdot \sin 0.621\pi$

$b \approx 7.072$

Answer 2

Answer:  a = -2.83 and b = 7.07.

Step-by-step explanation: I got this correct on Edmentum.

Also, to get the answer you first multiply $\left[\begin{array}{ccc}cos(\frac{3\pi }{4}) &(-sin\frac{3\pi }{4}) \\sin(\frac{3\pi }{4}) &cos(\frac{3\pi }{4}) \end{array}\right] by \left[\begin{array}{ccc}3\\-7\end{array}\right]$

The you multiply the answer which is $\left[\begin{array}{ccc}2\sqrt{2} \\5\sqrt{2} \end{array}\right]$  $by\ \left[\begin{array}{ccc}-1&0\\0&1\end{array}\right]$ then you get the answer $\left[\begin{array}{ccc}-2\sqrt{2} \\5\sqrt{2} \end{array}\right]$ or  -2.83 and 7.07. You can use a calculator like the one on ma th wa y to make multiplication easier, but when you do multiply always  put the 2x2 equation before the 2x1 to get another vector matrix.