Determine the Cartesian form of the plane whose equation in parametric form is: x = 2 + 3s-2t y = 1-s+5t z = −3+2s - t.

Zoe walks due west at 3km/hr on the deck of a boat which is sailing north at 15km/hr in still water (no current). Find the velocity of Zoe relative to the surface of the water. To begin your solution, use a cartesian plane with the y axis pointing north and express Vzb (the velocity of Zoe relative to the boat) and vbw (the velocity of the boat relative to the water) in component form.

Check if the planes z+3y+z=2 and 2x+y-z=-1 are parallel. If not, find a parametric equation of the line of intersection of the two planes. Find, correct to the nearest degrees, the angle between these two planes.

Find a set of parametric equations for the rectangular equation y=4x-2. Select one: a. x = 1-3, y=92 - 59t - 17 O b. xt, y = 4t-2 C. x=t, y = 9t²-5t-2 O d. x=t-3, y=4t+10 e. x=1+3, y=4t-10

Determine the Cartesian equation of a plane that has x-, y-, and z- intercepts 1/3, 1, and -1/2, respectively

Consider the equation z = x2 + y. (a) Describe the traces of the equation parallel to the xz-plane, both in equations and in words. (b) Sketch a graph of the equation. Сорy the axes as they aрреar below onto your own pаper.

Find the equation for the plane that passes through (2,4,-1) and contains the intersection of the planes x-y-4z=2 and -2x+y+2z = 3. (Hint: Find the parametric equation of the intersection of the two lines, choose two points on that line and then use the given point to write the equation of the plane passing through three points).

A particle moves linearly from the point (- 2,4) to (10,0) in 4 seconds. Find parametric equations to describe this motion.

Find a parametric equation for the line through the point (2,3, - 1) and perpendicular to the plane 8x + 3y + 3z = 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.