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

a = -1, b = -2.5

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
`(\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

a= -10 b= -2.5

Explanation: