# Given points A ( 2,-6,-1 ) and B (6,2,5) write the vector equation+ parametric equation of a line passing through points?

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### 1 Answer

You need to write the parametric equation of the line AB, hence, considering he pivot point A, yields:

`x = x_A + (x_B - x_A)*s => x = 2 + (6 - 2)*x => x = 2 + 4s`

`y = y_A + (y_B - y_A)*s => y = -6 + (2 + 6)*s => y = -6 + 8s`

`z = z_A + (z_B - z_A)*s => z = -1 + (5 + 1)*s => z = -1 + 6s`

**Hence, evaluating the parametric equation of the line passing through A and B yields `x = 2 + 4s, y = -6 + 8s, z = -1 + 6s` .**

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 = 4*bar i + 8*bar j + 6*bar ` k

Evaluating the vector equation yields:

`bar r = <2,-6,-1> + t*bar AB => bar r = <2,-6,-1> + t*<4,8,6>`

**Hence, evaluating the vector equation of the line passing through A and B yields **` bar r = <2,-6,-1> + t*<4,8,6>.`