Questions from General Calculus

Q: (a) Find a nonzero vector orthogonal to the plane through

(a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R, and (b) find the area of triangle PQR. P (1, 0, 1), Q (-2, 1, 3), R (4, 2, 5)

Q: A bicycle pedal is pushed by a foot with a 60-

A bicycle pedal is pushed by a foot with a 60-N force as shown. The shaft of the pedal is 18 cm long. Find the magnitude of the torque about P.

Q: (a). A horizontal force of 20 lb is applied to

(a). A horizontal force of 20 lb is applied to the handle of a gearshift lever as shown. Find the magnitude of the torque about the pivot point P. (b). Find the magnitude of the torque about P if the...

Q: Let v = 5j and let u be a vector with length

Let v = 5j and let u be a vector with length 3 that starts at the origin and rotates in the xy -plane. Find the maximum and minimum values of the length of the vector u × v. In what direction does u ×...

Q: (a). Let P be a point not on the plane

(a). Let P be a point not on the plane that passes through the points Q, R, and S. Show that the distance d from P to the plane is (b). Use the formula in part (a) to find the distance from the poin...

Q: For what value of x does the graph f(x)

For what value of x does the graph f(x) = ex – 2x of have a horizontal tangent?

Q: If a + b + c = 0, show that

If a + b + c = 0, show that a × b = b × c = c × a

Q: Prove that (a – b) × (a + b

Prove that (a – b) × (a + b) = 2 (a × b).

Q: Prove Property 6 of cross products, that is, a

Prove Property 6 of cross products, that is, a × (b × c) = (a ∙ c) b – (a ∙ b )c

Q: Use Exercise 50 to prove that a × (b ×

Use Exercise 50 to prove that a × (b × c) + b × (c × a) + c × (a × b) = 0 Exercise 50: Prove Property 6 of cross products, that is, a × (b × c) = (a ∙ c) b – (a ∙ b )c