Find the triple scalar product (u x v) ∙ w of the given vectors.u = -5i – 3j + 4k; v = 5i – 3j + 8k; w = 9i – 5j – 4k

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

Using Green’s Theorem, compute for the given path C. Assume C is closed and positive orientated. F = (9x + 2y)i + (8x – 6y)j; C is the region bounded above by y = -3×2 + 96 and below by in the first quadrant

Solve the problem.A 150-lb sign is hanging from the end of a hinged boom, supported by a cable inclined at 36° with the horizontal. Find the tension in the cable and the compression in the boom rounded to the nearest pound.

Find the triple scalar product (u x v) ∙ w of the given vectors.u = -5i – 3j + 4k; v = 5i – 3j + 8k; w = 9i – 5j – 4k

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.

Write the equation for the plane.The plane through the points P(-1, 7, -36) , Q(2, 6, -17) and R(1, -7, 30). 

Find the unit tangent vector of the given curve.r(t) = 3t2i – 12t2j + 4t2k

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

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