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

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

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((7)/(3) \right)`

`\theta \approx 1.629\pi`

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

`\theta' = \theta + (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((3\pi )/(4)) &(-sin(3\pi )/(4)) \\sin((3\pi )/(4)) &cos((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√(2) \\5√(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√(2) \\5√(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.