Questions from General Calculus

Q: A crane suspends a 500-lb steel beam horizontally by support

A crane suspends a 500-lb steel beam horizontally by support cables (with negligible weight) attached from a hook to each end of the beam. The support cables each make an angle of 60° with...

Q: Find the volume of the parallelepiped determined by the vectors a,

Find the volume of the parallelepiped determined by the vectors a, b, and c. a = 1, 2, 3 , b = −1, 1, 2 , c = 2, 1, 4

Q: Find the volume of the parallelepiped determined by the vectors a,

Find the volume of the parallelepiped determined by the vectors a, b, and c. a = i + j, b = j + k, c = i + j + k

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR

Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS. P (-2, 1, 0), Q (2, 3, 2), R (1, 4, -1), S (3, 6, 1)

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR

Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS. P (3, 0, 1), Q (-1, 2, 5), R (5, 1, -1), S (0, 4, 2)

Q: Use the scalar triple product to verify that the vectors u =

Use the scalar triple product to verify that the vectors u = i + 5 j - 2 k, v = 3i - j, and w = 5i + 9 j - 4 k are coplanar.

Q: Use the scalar triple product to determine whether the points A (

Use the scalar triple product to determine whether the points A (1, 3, 2), B (3, -1, 6), C (5, 2, 0), and D (3, 6, -4) lie in the same plane.

Q: A particle moves according to a law of motion s = f

A particle moves according to a law of motion s = f(t), t ≥ 0, where t is measured in seconds and s in feet. (a) Find the velocity at time t. (b) What is the velocity after 1 second?...

Q: Find the cross product a × b and verify that it is

Find the cross product a × b and verify that it is orthogonal to both a and b. a = 3i + 3j - 3k, b = 3i - 3j + 3k

Q: A wrench 30 cm long lies along the positive y-axis

A wrench 30 cm long lies along the positive y-axis and grips a bolt at the origin. A force is applied in the direction 0, 3, −4 at the end of the wrench. Find the magnitude of the force needed to su...