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

The correct answer is -10 and -2.5

Explanation:

Plato

Answer 2

a = 10

b = 2.5

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:

`<kx_1, kx_2>`

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

`<2.5* -1, 2.5* 4> \Rightarrow \vec B \bold{<-2.5, 10 > }`

Now, it is given that the vector is rotated by
`(\pi)/(2)` or
`90^\circ`.

The steps to find the resulting vector after the rotation of
`(\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