Write the equation for the plane.The plane through the points P(-1, 7, -44) , Q(2, -3, 20) and R(1, -1, 4). 

Find the angle between the given vectors. Round to the nearest tenth of a degree.u = i – j, v = 5i + 6j

Find the length of the curve with the given vector equation.r(t) = 3ti + j + k; 2≤ t ≤ 7

Find the length of the curve with the given vector equation.r(t) = 3ti + j + k; -9≤ t ≤ -6

If r(t) is the position vector of a particle in the plane at time t, find the indicated vector.Find the acceleration vector.r(t) = (7 ln(9t))i + (8t3)j

Solve the problem.A 250-lb sign is hanging from the end of a hinged boom, supported by a cable inclined at 39° with the horizontal. Find the tension in the cable and the compression in the boom rounded to the nearest pound.

Find the potential function f for the field F.F(x,y,z) = 9i + -ezj – yezk

Find the requested partial derivative of the given function. f(x, y) = x ln (y – x) Find

Solve the problem. Unless stated otherwise, assume that the projectile flight is ideal, that the launch angle is measured from the horizontal, and that the projectile is launched from the origin over a horizontal surfaceA projectile is fired at a speed of 1160 m/sec at an angle of 36°. How long will it take to get 29 km downrange? Round your answer to the nearest whole number.

Using Green’s Theorem, compute for the given path C. Assume C is closed and positive orientated. F = (-5x + 3y)i + (8x – 4y)j; C is the region bounded above by y = -4×2 + 32 and below by in the first quadrant