distance (1,2,3),(4,6,3) — step-by-step solution

The distance is the norm of the difference of the points: the square root of the sum of the squared coordinate differences

Let's evaluate:

‖ (4, 6, 3) - (1, 2, 3) ‖

ⅰ

(4, 6, 3) - (1, 2, 3)

(4 - 1, 6 - 2, 3 - 3)

‖ (4 - 1, 6 - 2, 3 - 3) ‖

ⓘ Start from

4

and move back

1

on the number line:

4 - 1

3

■Start from

6

and move back

2

on the number line:

6 - 2

4

■Start from

3

and move back

3

on the number line, down to zero:

3 - 3

0

‖ (3, 4, 0) ‖

ⅰ

‖ (3, 4, 0) ‖

\sqrt{3^{2} + 4^{2} + 0^{2}}

\sqrt{3^{2} + 4^{2} + 0^{2}}

ⓘ Powers are computed before multiplications, additions and subtractions. An integer power is a repeated product:

3^{2}

3 \times 3

9

4^{2}

4 \times 4

16

■Adding 0 changes nothing:

4^{2} + 0

4^{2}

\sqrt{9 + 16}

ⓘ Parentheses are computed first:

9 + 16

25

\sqrt{25}

ⓘ The square root of a number is the positive number whose square is that number:

\sqrt{25}

5

;

5^{2}

25

▶Distance:

5