Question

The vector is first dilated by a factor of 2.5 and then rotated by radians. If the resulting vector is , then a =_____ and b = ____.

Answer 1

Answer:

a = 10

b = 2.5

Step-by-step explanation:

The given vector is

<-1, 4>

Let $\vec A$ represents <-1, 4>.

First, the dilation is done by a factor of 2.5.

If the dilation of a vector <$x_1$, $x_2$> is done by a factor k:

Then the resulting vector becomes:

The resulting $\vec B$ as per above explanation:

$\Rightarrow \vec B \bold{ }$

Now, it is given that the vector is rotated by $\frac{\pi}{2}$ or $90^\circ$.

The steps to find the resulting vector after the rotation of $\frac{\pi}{2}$ or $90^\circ$, we can use the simple method:

Step 1:  Multiply the $x$ value with -1.

i.e. the vector now becomes <2.5, 10> (Negative sign of x value removed).

Step 2: Swap the values of $x$ and $y$.

So, the resulting vector is:

<10, 2.5>

In other form, we can represent the above vector as:

$\left[\begin{array}{c}10&2.5\end{array}\right]$

Comparing with $\left[\begin{array}{c}a&b\end{array}\right]$

a = 10

b = 2.5