Please solve only number 4 showing work.
1 : 2x -y + 2z = 3, and 2 : 2x + 2y - z = 3. Find the equation of the plane 3 in R3, which passes through P = (1, 1, 1) and is orthogonal to the planes 1 and 2. Find the volume of the parallelepiped U: t1a1 + t2a2 + t3a3 : 0 t1, t2, t3 1 with sides the vectors a1 = (5, 2, 4), a2 = (2, 1, 2), and a3 = (5, 1, 3). Parameterize the plane curve X : x4 + y4 = x2y + xy2. Find the velocity vector v(t) = X'(t) and the acceleration v X"(t) at each point X(t) of the curve X : X(t) = (2cos(t), sin(t), t), 0 t 2 pi,
Show transcribed image text 1 : 2x -y + 2z = 3, and 2 : 2x + 2y - z = 3. Find the equation of the plane 3 in R3, which passes through P = (1, 1, 1) and is orthogonal to the planes 1 and 2. Find the volume of the parallelepiped U: t1a1 + t2a2 + t3a3 : 0 t1, t2, t3 1 with sides the vectors a1 = (5, 2, 4), a2 = (2, 1, 2), and a3 = (5, 1, 3). Parameterize the plane curve X : x4 + y4 = x2y + xy2. Find the velocity vector v(t) = X'(t) and the acceleration v X"(t) at each point X(t) of the curve X : X(t) = (2cos(t), sin(t), t), 0 t 2 pi,