Explain why the normalized vector A has no fraction
Explain why the normalized vector A has no fraction
user
Explain why the normalized vector A has no fractional components.

#### Solution

Let A be a normalized vector.

Then, `|A| = 1`

`|A| = sqrt(A_1^2 + A_2^2 + A_3^2)`

`1 = sqrt(A_1^2 + A_2^2 + A_3^2)`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`
assistant
Explain why the normalized vector A has no fraction
user
Explain why the normalized vector A has no fractional components.

#### Solution

Let A be a vector with fractional components.

Then, A = `(a_1/b, a_2/b, a_3/b)`

`therefore |A| = sqrt((a_1/b)^2 + (a_2/b)^2 + (a_3/b)^2)`

`= sqrt((a_1^2)/b^2 + (a_2^2)/b^2 + (a_3^2)/b^2)`

`= sqrt((a_1^2 + a_2^2 + a_3^2)/b^2)`

`= sqrt((a_1^2 + a_2^2 + a_3^2)/(a_1^2 + a_2^2 + a_3^2))`

`= sqrt(1) = 1`

`therefore |A| = 1`

`therefore A = (a_1/b, a_2/b, a_3/b)`

`therefore A = (a_1/b, a_2/b, a_3/b)`

`therefore A = (a_1/b, a_2/b, a_3/b)`

`therefore A = (a_1/b, a_2/b, a_3/b)`

`therefore A = (a_1/b, a_2/b, a_3/b)`

`therefore A = (a_1/b, a_2/b, a_3/b)`

`therefore A = (a_1/b, a_2/b, a_3/b)`

`therefore A = (a_1/b, a_2/b, a_3/b)`

`therefore A = (a_1/b, a_2/b, a_3/b)`

`therefore A = (a_1/b, a_2/b, a_3/b)`

`therefore A = (a_1/b, a_2/b, a_3/b)`

`therefore A = (a_1/b, a_2/b, a_3/b)`

`therefore A = (a_1/b, a_2/b, a_3/b)`

`therefore A = (a_1/b, a_2/b, a_3/b)`

`therefore A = (a_1/b, a_2/b, a_3/b)`

`therefore A = (a
assistant
Explain why the normalized vector A has no fraction
user
Explain why the normalized vector A has no fractional components.

#### Solution

Let A be a normalized vector.

Then, `|A| = 1`

`|A| = sqrt(A_1^2 + A_2^2 + A_3^2)`

`1 = sqrt(A_1^2 + A_2^2 + A_3^2)`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`A_1^2 + A_2^2 + A_3^2 = 1`

`
assistant