Vectors: Magnitude & Direction

How do you convert a vector to a unit vector?

• Multiply the vector by its magnitude.

• Divide the vector by its magnitude.

• Add the vector to its magnitude.

• Subtract the magnitude from the vector.

How do you find the resultant vector of two vectors?

• R = A_x + B_x, A_y + B_y

• R = A_x - B_x, A_y - B_y

• R = A_x * B_x, A_y * B_y

• R = A_x / B_x, A_y / B_y

What is the magnitude of the vector <10, -8>?

• 10.00

• 12.81

• 14.42

• 8.00

How do you add two vectors graphically?

• Place the tail of the second vector at the head of the first vector and draw a new vector from the tail of the first to the head of the second.

• Simply add the magnitudes of the two vectors together without considering their directions.

• Draw both vectors starting from the same point and connect their endpoints with a straight line.

• Add the two vectors by placing them parallel to each other and drawing a line from the start of the first to the end of the second.

How do you find the angle between two vectors?

• cos(θ) = (A • B) / (|A| |B|)

• θ = A + B

• θ = |A| + |B|

• cos(θ) = |A| / |B|

What is the difference between scalar and vector quantities?

• Scalar quantities have only magnitude (e.g., temperature), while vector quantities have both magnitude and direction (e.g., velocity).

• Scalar quantities have both magnitude and direction, while vector quantities have only magnitude.

• Scalar quantities are always positive, while vector quantities can be negative.

• Scalar quantities can be represented graphically, while vector quantities cannot.

How do you find the magnitude of a vector represented as ?

• √(x² + y²)

• x + y

• x - y

• √(x² - y²)

What is the significance of the direction of a vector?

• The direction of a vector indicates the path along which the quantity acts, essential for understanding motion and forces.

• The direction of a vector is irrelevant to its magnitude and can be ignored.

• The direction of a vector only matters in two-dimensional space.

• The direction of a vector is only important in static situations.

What is the definition of a vector?

• A quantity that has only magnitude.

• A quantity that has both magnitude and direction.

• A quantity that has only direction.

• A quantity that is always positive.

Given points A(2, 4) and B(-8, 7), how do you find the vector AB?

• AB = <-10, 3>

• AB = <6, 3>

• AB = <10, -3>

• AB = <-6, -3>