Answer:
a = 10
b = 2.5
Explanation:
The given vector is
<-1, 4>
Let
represents <-1, 4>.
First, the dilation is done by a factor of 2.5.
If the dilation of a vector <
,
> is done by a factor k:
Then the resulting vector becomes:

The resulting
as per above explanation:

Now, it is given that the vector is rotated by
or
.
The steps to find the resulting vector after the rotation of
or
, we can use the simple method:
Step 1: Multiply the
value with -1.
i.e. the vector now becomes <2.5, 10> (Negative sign of x value removed).
Step 2: Swap the values of
and
.
So, the resulting vector is:
<10, 2.5>
In other form, we can represent the above vector as:
![\left[\begin{array}{c}10&2.5\end{array}\right]](https://img.qammunity.org/2021/formulas/mathematics/college/rdwnpdmqfakijx8avc11cx3sqg2gb0hbsm.png)
Comparing with
![\left[\begin{array}{c}a&b\end{array}\right]](https://img.qammunity.org/2021/formulas/mathematics/college/ed17uoxd3nsz2d9umla4xemb78hlibkj0d.png)
a = 10
b = 2.5