Calculus III: Two Dimensional Vectors (Level 6 of 13)

The video tutorial covers the algebraic representation of vector operations, focusing on scalar multiplication, vector addition, and subtraction. It explains how to perform these operations algebraically, discusses the concept of parallel vectors, and provides examples to illustrate scalar multiplication. The tutorial emphasizes the computational convenience of algebraic methods and their applications in understanding parallel vectors, which are crucial in multivariable calculus.

What happens to the components of a vector when it is multiplied by a scalar?

• They are divided by the scalar.

• They are added to the scalar.

• They remain unchanged.

• They are multiplied by the scalar.

If a vector is multiplied by a negative scalar, what happens to its direction?

• It becomes perpendicular.

• It becomes zero.

• It remains the same.

• It reverses direction.

How can you determine if two vectors are parallel?

• By checking if they have the same magnitude.

• By checking if they are perpendicular.

• By checking if one is a scalar multiple of the other.

• By checking if they have the same initial point.

Which of the following vectors is parallel to vector v if vector v = (3, 4)?

• (6, 8)

• (3, -4)

• (4, 3)

• (0, 0)

What is the result of multiplying vector v = (3, 4) by 0?

• (6, 8)

• (-3, -4)

• (3, 4)

• (0, 0)

If vector z = (3, 2), which vector is not parallel to z?

• (6, 4)

• (9, 6)

• (1.5, 1)

• (1, 2)

What is the x-component of the resultant vector when vector v = (1, 2) is added to vector u = (2, 3)?

• 4

• 3

• 2

• 1

How do you find the y-component of the resultant vector when subtracting vector u = (2, 3) from vector v = (1, 2)?

• Divide the y-component of v by u.

• Multiply the y-components of both vectors.

• Subtract the y-component of u from v.

• Add the y-components of both vectors.

Which law can be used to geometrically find the sum of two vectors?

• Triangle Law

• Law of Sines

• Pythagorean Theorem

• Law of Cosines

What is the y-component of the resultant vector when vector v = (1, 2) is added to vector u = (2, 3)?

• 2

• 3

• 5

• 4