Dear Tutor,

please find below my home work need to be answered

1. Find the equation of the plane that passes through the points (2, 1, 1) and (-1, 3, 2), and both also perpendicular to the plane 2x + 3y - 4z = 3

2. Sketch the curve of the vector function r(t) = 2 sin t i + 3 cos t j on the xy coordinate plane.

3. Find the values of r(/4), r'(/4), and r''(/4), if r(t) = cos³t i + sin³t j

4. An object is moving with initial position and velocity given by r(0) = i + 2j + k and

v(0) = i + 2k, respectively. The object's acceleration at time t is a(t) = 6t i + j + 2k.

Determine the position and velocity of the object each time.

Thanks