# We have two points A ( 3,4,-5 ) and B (7,-3,8) what are the parametric equation and the vector equation of a line D passing through A et B.

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Expert Answers

sciencesolve | Certified Educator

You need to find the direction vector of the line AB, such that:

`bar (AB) = (x_B - x_A)bar i + (y_B - y_A)bar j + (z_B - z_A)bar k`

`bar (AB) = (7 - 3)bar i + (-3 - 4)bar j + (8 + 5)bar k`

`bar (AB) = 4bar i - 7bar j + 13bar k`

You need to find the parametric equations of the line AB, such that:

`x = x_A + (x_B - x_A)*t => x = 3 + 4t`

`y = y_A + (y_B - y_A)*t => y = 4 - 7t `

`z = z_A + (z_B - z_A)*t => z = -5 + 13t`

**Hence, evaluating the parametric equations of the line AB, yields **`x = 3 + 4t , y = 4 - 7t , z = -5 + 13t.`