Vectors

Front

What is a vector?

Back

A vector is a quantity that has both magnitude and direction, represented graphically by an arrow.

Front

How do you find the magnitude of a vector \( \langle a, b \rangle \)?

Back

The magnitude is calculated using the formula: \( \sqrt{a^2 + b^2} \).

Front

What is the component form of a vector from point A (x1, y1) to point B (x2, y2)?

Back

The component form is given by \( \langle x2 - x1, y2 - y1 \rangle \).

Front

Find the magnitude of the vector \( \langle 2, -3 \rangle \).

Back

The magnitude is \( \sqrt{2^2 + (-3)^2} = \sqrt{13} \).

Front

Given points A (2, 4) and B (-8, 7), find the vector AB.

Back

The vector AB is \( \langle -8 - 2, 7 - 4 \rangle = \langle -10, 3 \rangle \).

Front

What is the vertical component of a vector?

Back

The vertical component is the y-coordinate of the vector in its component form.

Front

Given points R (-12, 4) and S (28, -17), find the vector RS.

Back

The vector RS is \( \langle 28 - (-12), -17 - 4 \rangle = \langle 40, -21 \rangle \).

Front

How do you calculate the vertical component of velocity from a vector?

Back

The vertical component of velocity is the second element of the vector representing velocity.

Front

Find the magnitude of the vector \( \langle -3, 4 \rangle \).

Back

The magnitude is \( \sqrt{(-3)^2 + 4^2} = 5 \).

Front

What does the term 'component form' refer to in vectors?

Back

Component form refers to expressing a vector in terms of its horizontal and vertical components, typically as \( \langle x, y \rangle \).