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In Exercises 13-16, find a
15. 3(x - 4) - 8(y - 1) + llz = 0
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- Find the linear equation of the plane through the point (2, −2, 6) and with normal vector j+2k.Create the vector & parametric equations for the line that passes through the point L₁ x 3- 2t (0, 1, -2) and is parallel to the line y z = = - 5t - 1-t.Find the equation of the plane in xyz-space through the point P = (3, 5, 3) and perpendicular to the vector n = = (−1, −3, 3). 2 =
- Represent the line segment from P(−2, −3, 8), Q(5, 1, −2) by a vector-valued function and by a set of parametric equations.Suppose that a plane contains the points (5, 0, 0) and (0, 3, 1) and the line with the vector equation r = t < 2.5, 1.5, 0.5 >. What is the equation of the line? Please explain your steps and show work.Develop vector and parametric equations for the line through (7,2,-1) and parallel to r = (4,7,0) + s(4,-5,1). Please answer Thank you.
- Find an equation of the plane that passes through (4,-1,2) and has a normal vector perpendicular to both ⟨ 3 , 1 , 1 ⟩ and ⟨ 5 , − 2 , 0 ⟩ . Simplify to general form.Find the vector equation of a line passing through (5,1,3) and perpendicular to the plane 3x - 2y + z = 7.Find the general equation of the plane which goes through the point (3,1,0) and is perpendicular to the vector < 1, −1, 2 >