Question

PLATO: Type the correct answer in each box. The vector is first dilated by a factor of 2.5 and then rotated by pi/2 radians. If the resulting vector is [a / b], then a = __ and b = __

Answer 1

Answer:

a = -1, b = -2.5

Step-by-step explanation:

Rule for the dilation of a vector $\binom{x}{y}$ by a scale factor of k is,

(x, y) → (kx, ky)

BY using this rule for a vector $\binom{-1}{4}$ by a scale factor of 2.5

$\binom{-1}{4}$ → $\binom{-2.5}{1}$

Followed by the rotation by 90° Or $\frac{\pi }{2}$ radians,

Rule for rotation of a vector by 90° is,

(x, y) → (-y, x)

By this rule vector $\binom{-2.5}{1}$ will become,

$\binom{-2.5}{1}$ → $\binom{-1}{-2.5}$

If we represent this vector by $\binom{a}{b}$,

Then a = -1 and b = -2.5 will be the answer.

Answer 2

Answer:

a= -10 b= -2.5

Step-by-step explanation: