Day 10 (3/28/25) Vectors and Dot Products

Front

What is a vector?

Back

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

Front

What is the dot product of two vectors?

Back

The dot product is a scalar value obtained by multiplying the magnitudes of two vectors and the cosine of the angle between them.

Front

How do you find the angle between two vectors?

Back

Use the formula: cos(θ) = (A • B) / (||A|| ||B||), where A • B is the dot product of vectors A and B.

Front

What does ||v|| represent?

Back

||v|| represents the magnitude (length) of vector v.

Front

How do you calculate the magnitude of a vector v = ai + bj?

Back

The magnitude is calculated as ||v|| = √(a² + b²).

Front

What are equivalent vectors?

Back

Equivalent vectors are vectors that have the same magnitude and direction, regardless of their position.

Front

What is the position vector?

Back

A position vector represents the position of a point in space relative to an origin, expressed in terms of unit vectors i and j.

Front

How do you express a vector in terms of i and j?

Back

A vector can be expressed as v = ai + bj, where a and b are the components along the x-axis and y-axis, respectively.

Front

What is the formula for the dot product of two vectors A and B?

Back

A • B = Ax * Bx + Ay * By, where Ax and Ay are the components of vector A, and Bx and By are the components of vector B.

Front

What is the significance of the angle between two vectors?

Back

The angle between two vectors indicates the relationship between their directions; it affects the value of their dot product.