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- Find the vector and parametric equations for the line through the point P(1,1,3) and parallel to the vector -2i + 1j + 2k 1. Vector Form r=(<_,_,3>)+t(<_,_,2>) 2. Parametric form (parameter t, and passing through P when t=0): x=x(t)= y=y(t)= z=z(t)=Find 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 the vector and parametric equations for the line through the point P=(0,-3,1) and the point Q=(-2,-4,2) 1. Vector Form r=(<_,_,1>)+t(<_,_,1>) 2. Parametric form (parameter t, and passing through P when t=0): x=x(t)= y=y(t)= z=z(t)=
- (A) Find the parametric equations for the line through the point P = (-2, 5, -3) that is perpendicular to the plane 3x−1y+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 = ( , , )4. Find the parametric equation of the line through (1, 0, -2) and parallel to the line ⅓ (x – 4) = ½ (y) = z + 2.Find a set of parametric equations for the line passing through the point (2, 0, 9) that is parallel to the plane given by x + y + z = 5, and perpendicular to the line x = −1 + t, y = 1 + t, z = 10 − t.
- 16) Find a vector equation and parametric equations for the line segment that joins P to Q. P(1, 0, 1), Q(2, 3, 1)Find the parametric equations for the line through the point (1, 7, 2) that is parallel to the plane x+ y + z = 10 and perpendicular to the line x = 3 + t, y = -18 - t, z = 5t.Find the vector and parametric equations for the line through the point P(2, 2, -2) and orthogonal to the plane −2x−4y−2z=1. Vector Form: r=⟨ , , -2 ⟩+t⟨ , , -2⟩ Parametric form (parameter t, and passing through P when t = 0):x=x(t)=y=y(t)=z=z(t)=
- Find parametric equations for the line through the origin parallel to the vector 4j+9k. Let z=9t. x___, y____, z_____, −∞<t<∞ (Type expressions using t as the variable.)Find a parametric equation for the line through the point (−7,4,−7) and perpendicular to the plane 7x+4y+9z=5 which is written using the coordinates of the given point and the coefficients of x, y, and z in the given equation of the plane.