Unit 1 Review

Front

What is the formula for the volume of a parallelepiped?

Back

The volume of a parallelepiped can be calculated using the scalar triple product: V = |t · (u × v)|, where t, u, and v are the vectors defining the parallelepiped.

Front

What is torque and how is it calculated?

Back

Torque (τ) is a measure of the rotational force applied to an object. It is calculated using the formula: τ = r × F, where r is the distance from the axis of rotation to the point of force application, and F is the force applied.

Front

How do you calculate work done when a force is applied?

Back

Work (W) is calculated using the formula: W = F × d × cos(θ), where F is the force applied, d is the distance moved in the direction of the force, and θ is the angle between the force and the direction of motion.

Front

What does it mean for two vectors to be orthogonal?

Back

Two vectors are orthogonal if their dot product is zero. This means they are at a right angle (90 degrees) to each other.

Front

Calculate the volume of the parallelepiped defined by the vectors t = <1, 1, -4>, u = <-3, 2, 7>, v = <2, -6, 8>.

Back

The volume is 40.

Front

Calculate the torque applied to a wrench when a 15N force is applied 50cm from the axis of rotation and moves 10cm as it turns.

Back

The torque applied is 7.5 Nm.

Front

If a force of 200N is applied over a distance of 10m, how much work is done?

Back

The work done is 1800 J.

Front

What is the dot product of two vectors and how is it calculated?

Back

The dot product of two vectors a and b is calculated as a · b = |a| |b| cos(θ), where θ is the angle between the vectors.

Front

What is the significance of the scalar triple product in vector analysis?

Back

The scalar triple product gives the volume of the parallelepiped formed by three vectors and indicates whether the vectors are coplanar (if the result is zero).

Front

Define the term 'vector'.

Back

A vector is a quantity that has both magnitude and direction, such as force, velocity, or displacement.