Calculus III: The Cross Product (Level 3 of 9)

The video tutorial covers the cross product of vectors using geometric and component definitions. It includes examples to find the magnitude and direction of cross products, using the right-hand rule for direction. The tutorial also demonstrates verifying orthogonality of cross products through dot products, and explains cross products in unit vector form.

What is the magnitude of the cross product of two vectors if their magnitudes are 5 and 5, and the angle between them is 60 degrees?

• 50√3

• 25

• 50

• 25√3

Using the right-hand rule, if vector a is directed to the right and vector b is directed upwards, where does the cross product vector point?

• Out of the page

• Into the page

• To the left

• Downwards

If the angle between vector b and vector a is 30 degrees, what is the magnitude of their cross product given their magnitudes are 4 and 6?

• 24

• 36

• 48

• 12

When using the right-hand rule for vector b crossed with vector a, which direction does the thumb point if vector b is directed upwards and vector a is directed to the right?

• Downwards

• Out of the page

• To the left

• Into the page

What is the angle between vector v in the xy-plane and vector u in the positive k direction?

• 180 degrees

• 0 degrees

• 45 degrees

• 90 degrees

For vectors v and u, if vector v is in the xy-plane and vector u is in the positive k direction, what is the z component of their cross product?

• Negative

• Positive

• Undefined

• Zero

What is the first step in finding the cross product of vectors a and b using the component definition?

• Find the angle between vectors

• Use the right-hand rule

• Set up a 3x3 determinant

• Calculate the dot product

How can you verify that the cross product of two vectors is orthogonal to the original vectors?

• By calculating the dot product

• By checking the magnitudes

• By finding the angle between them

• By using the right-hand rule

In the fifth example, what is the x component of vector b if it is given in standard unit vector form and has no i hat value?

• 1

• 0

• Depends on vector a

• Undefined

What is a common mistake students make when calculating the cross product using determinants?

• Misplacing the unit vectors

• Using the wrong angle

• Incorrectly applying the right-hand rule

• Forgetting the negative sign in the j component