Answer:
<em>a = 10</em>
<em>b = 2.5</em>
Step-by-step 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 <em>k:</em>
Then the resulting vector becomes:
![](https://tex.z-dn.net/?f=%3Ckx_1%2C%20kx_2%3E)
The resulting
as per above explanation:
![\Rightarrow \vec B \bold{ }](https://tex.z-dn.net/?f=%3C2.5%5Ctimes%20-1%2C%202.5%5Ctimes%204%3E%20%5CRightarrow%20%5Cvec%20B%20%5Cbold%7B%3C-2.5%2C%2010%20%3E%20%7D)
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://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D10%262.5%5Cend%7Barray%7D%5Cright%5D)
Comparing with ![\left[\begin{array}{c}a&b\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Da%26b%5Cend%7Barray%7D%5Cright%5D)
<em>a = 10</em>
<em>b = 2.5</em>