Find the triple scalar product (u x v) ∙ w of the given vectors.u = -5i – 3j + 4k; v = 5i – 3j + 6k; w = 10i – 6j – 5k

Find the angle between the given vectors. Round to the nearest tenth of a degree.u = i – j, v = 3i + 5j

True or False:If  the and , the appropriate decision is to REJECT the null hypothesis.

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

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

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 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.

Evaluate the line integral along the curve C.ds, C is the curve r(t) = (4 sin t)i + (4 cos t)j + 12tk, 2 ≤ t ≤ 4

During what age range is brain growth the fastest? At what age does the brain finish pruning the prefrontal cortex?