Find the distance d between the points P19 4 8 and P210 7 2

Find the distance d between the points P₁=(9, 4, 8) and P₂=(10, 7, 2) by first finding the vector v from P₁ to P₂, then finding the length of v. Use the square root symbol \'\' where needed to give an exact value for your answer.

VECTOR V= (...)

DISTANCE = (...)

Solution

The vector v between the points P₁ = (9,-4,8) and P₂ = (-10,7,-2) is ( -10 -9, 7-(-4), -2-8 ) = (-19, 11,-10). Then the distance from the point P1 to the point P₂ is ||v|| = [ (-19)²+(11)²+(-10)²] = ( 361+ 121+100) = 582.