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- Give a vector parametric equation for the line through the point (3,4,−2) that is parallel to the line ⟨−4−5t,3+4t,−2−3t⟩Find both the parametric and vector equation of the line segment between (−2, 3) and (5, −1) where 0 ≤ t ≤ 1. Please show all your work.Find parametric equations of the line through the point (5, 0,−2) that is parallel to the planes x −4y + 2z = 0and 2x + 3y −z +1 = 0.
- Find the parametric equations for the line through the point P = (-1, 4, -4) that is perpendicular to the plane 2x−4y−2z=1.2x−4y−2z=1.Use "t" as your variable, t = 0 should correspond to P, and the velocity vector of the line should be the same as the standard normal vector of the plane. x = y = z = (B) At what point Q does this line intersect the yz-plane? Q = ( , , )Find parametric and vector equation for line segment which reach (2, 2.4 , 3.5) point and parallel to the 3i + 2j -k vector a) (1+3t)i + (4+2t)j + (3-t)k b) (2+3t)i + (2.4+2t)j + (3.5-t)k c) (1+3t)i + (2+t)j - (3.5-2t)k d) (2t)i + (1.5-2t)j + (3.5-1t)kFind the set of symmetric and parametric equations of the line passing through the point P(3, 4, 1) that is parallel to the plane 3x−2y −z −4 = 0 and perpendicular to the line 2x = −y/2 = −3z.
- Find parametric equations for the normal line to the surface z=-7x2 -9y2 at the point (2,1,-37)This Linear Algebra and Multivariate Calculus Course , . . Find the parametric equation of line that passes throught the point (1,-2,4) and is parallel to the vector v = [2,4,-4] ?Find the vector equation of the plane taking into account that 4x - y - z = 3