Questions from General Calculus

Q: Find the magnitude of the resultant force and the angle it makes

Find the magnitude of the resultant force and the angle it makes with the positive x-axis.

Q: Find |u × v | and determine whether u × v

Find |u × v | and determine whether u × v is directed into the page or out of the page.

Q: If a = 2, −1, 3 and

If a = 2, −1, 3 and b = 4, 2, 1 , find a × b and b × a.

Q: If a = 1, 0, 1 , b =

If a = 1, 0, 1 , b = 2, 1, −1 , and c = 0, 1, 3 , show that a × (b × c) ≠ (a × b) × c.

Q: Find two unit vectors orthogonal to both 3, 2,

Find two unit vectors orthogonal to both 3, 2, 1 and −1, 1, 0 .

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 = 4, 3, −2 , b = 2, −1, 1

Q: Find two unit vectors orthogonal to both j - k and i

Find two unit vectors orthogonal to both j - k and i + j.

Q: Show that 0 × a = 0 = a × 0 for

Show that 0 × a = 0 = a × 0 for any vector a in V3.

Q: Show that (a × b) ∙ b = 0 for

Show that (a × b) ∙ b = 0 for all vectors a and b in V3.

Q: Prove the property of cross products (Theorem 11). Property

Prove the property of cross products (Theorem 11). Property 1: a × b = -b × a