Question

Find the magnitude of a vector with initial point A(3, 4, 10) and terminal point B(8, 4, –2).

A: 0
B: 13
C: 8
D:16
​

Answer 1

B

Explanation:

Use the distance formula in 3 dimensions

d =
`\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2+(z_(2)-z_(1))^2 }`

with (x₁, y₁, z₁ ) = (3, 4, 10) and (x₂, y₂, z₂ ) = (8, 4, - 2)

d =
`√((8-3)^2+(4-4)^2+(-2-10)^2)`

=
`√(5^2+0^2+(-12)^2)`

=
`√(25+144)`

=
`√(169)`

= 13 → B