Question

Given R(3, 7,-1),S(10,-4,0) find an ordered triple that represents RS and find the magnitude of RS.

Answer 1

see explanation

Explanation:

RS = s-r (s, r are the position vectors of R and S )

RS = (10, - 4, 0 ) - (3, 7, - 1) = (10 - 3, -4 - 7, 0 - (- 1)) = (7, - 11, 1 )

| RS | =
`√(7^2+(-11)^2+1^2)` =
`√(171)` = 3
`√(19)`

Answer 2

`| RS | =3√(19)`

Explanation:

Given points are R ( 3 ,7, -1 ) and S (10 ,-4, 0)

The distance between R and S

RS = (10 ,-4, 0) - ( 3 ,7, -1 )

= (10 - 3, -4 - 7, 0 - (- 1))

= (7, - 11, 1 )

Magnitude is calculated as:

`| RS | =\sqrt{(7)^(2) + (-11)^(2) + (1)^(2)}`

`| RS | =√(49 + 121 + 1)`

`| RS | =√(171)`

`| RS | =3√(19)`