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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=__

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xero099

Answer:

[tex]a \approx -2.826[/tex], [tex]b \approx 7.072[/tex]

Step-by-step explanation:

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

[tex]r = \sqrt{3^{2}+ (-7)^{2}}[/tex]

[tex]r \approx 7.616[/tex]

[tex]\theta \approx 2\pi - \tan^{-1}\left(\frac{7}{3} \right)[/tex]

[tex]\theta \approx 1.629\pi[/tex]

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

[tex]\theta' = \theta + \frac{3\pi}{4}[/tex]

[tex]\theta' = 2.379\pi[/tex]

Which is coterminal with [tex]\theta'' = 0.379\pi[/tex]. The reflection across y-axis is:

[tex]\theta''' = \pi - \theta''[/tex]

[tex]\theta''' = 0.621\pi[/tex]

The equivalent vector in rectangular coordinates is:

[tex]a = 7.616\cdot \cos 0.621\pi[/tex]

[tex]a \approx -2.826[/tex]

[tex]b = 7.616\cdot \sin 0.621\pi[/tex]

[tex]b \approx 7.072[/tex]

elpink25

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 [tex]\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][/tex]

The you multiply the answer which is [tex]\left[\begin{array}{ccc}2\sqrt{2} \\5\sqrt{2} \end{array}\right][/tex]  [tex]by\ \left[\begin{array}{ccc}-1&0\\0&1\end{array}\right][/tex] then you get the answer [tex]\left[\begin{array}{ccc}-2\sqrt{2} \\5\sqrt{2} \end{array}\right][/tex] 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.

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