Vectors! More practice

Front

What is the magnitude of a vector?

Back

The magnitude of a vector is its length, calculated using the formula √(x² + y²) for a vector represented as .

Front

How do you find the resultant vector of two vectors?

Back

To find the resultant vector, add the corresponding components of the vectors. For example, if A = and B = , then the resultant R = .

Front

What is the direction of a vector?

Back

The direction of a vector is the angle it makes with the positive x-axis, calculated using the formula θ = tan⁻¹(y/x).

Front

How do you write a vector in component form?

Back

A vector in component form is expressed as , where x is the horizontal component and y is the vertical component.

Front

What is the formula to calculate the magnitude of a vector ?

Back

The formula is |v| = √(x² + y²).

Front

If a vector is represented as <3, 4>, what is its magnitude?

Back

The magnitude is 5, calculated as √(3² + 4²) = √(9 + 16) = √25 = 5.

Front

What does a negative component in a vector indicate?

Back

A negative component indicates direction; for example, a negative x-component means the vector points left.

Front

How do you determine the angle of a vector in standard position?

Back

Use the formula θ = tan⁻¹(y/x) and adjust based on the quadrant the vector is in.

Front

What is the significance of the resultant vector?

Back

The resultant vector represents the combined effect of two or more vectors, showing the overall direction and magnitude.

Front

What is the component form of the vector with a magnitude of 10 and direction of 30 degrees?

Back

The component form is <10cos(30), 10sin(30)> = <5√3, 5>.