Vectors - Dot Product

Front

What is the dot product of two vectors?

Back

The dot product of two vectors is a scalar value obtained by multiplying their corresponding components and summing the results. It is denoted as A · B = Ax * Bx + Ay * By.

Front

Calculate the dot product of the vectors <1, -2> and <3, 2>.

Back

The dot product is 1*3 + (-2)*2 = 3 - 4 = -1.

Front

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

Back

The magnitude of a vector is calculated using the formula ||v|| = √(x² + y²).

Front

Find the magnitude of the vector <-5, 12>.

Back

The magnitude is √((-5)² + 12²) = √(25 + 144) = √169 = 13.

Front

What is the angle between two vectors if their dot product is zero?

Back

If the dot product of two vectors is zero, the angle between them is 90 degrees, indicating that they are orthogonal.

Front

How do you find the angle between two vectors A and B?

Back

The angle θ between two vectors A and B can be found using the formula: cos(θ) = (A · B) / (||A|| * ||B||).

Front

What does it mean if the dot product of two vectors is negative?

Back

If the dot product of two vectors is negative, it indicates that the angle between them is greater than 90 degrees.

Front

What is the geometric interpretation of the dot product?

Back

The dot product represents the projection of one vector onto another and is related to the cosine of the angle between them.

Front

Calculate the dot product of the vectors <3, 4> and <4, -3>.

Back

The dot product is 3*4 + 4*(-3) = 12 - 12 = 0.

Front

What is the significance of the dot product in physics?

Back

In physics, the dot product is used to calculate work done when a force is applied along a displacement.