# Finding the Scalar Triple Product of Three Vectors

• Ashutosh
In summary, to find the value of m that will result in a volume of 24 for a parallelopiped with edges given by (2î + 3j^+ 4k^), 4j^, and (5j^ + mk^), you can use the formula for the scalar triple product of three vectors. This formula is not the same as the dot product of three vectors.
Ashutosh

## Homework Statement

The edges of a parallelopiped are given by the vectors (2î + 3j^+ 4k^), 4j^ and (5j^ + mk^). What should be the value of m inorder that the volume of the parallelopiped be 24?

## The Attempt at a Solution

Volume of the parallelopiped is the scalar triple product of three vectors. I want to know the formula or method of finding dot product of three vectors.

The scalar triple product is not a dot product of three vectors, it is ##\vec u \cdot (\vec v \times \vec w)##.

Ashutosh
Orodruin said:
The scalar triple product is not a dot product of three vectors, it is ##\vec u \cdot (\vec v \times \vec w)##.
Thank You.

## 1. What is motion in a plane?

Motion in a plane refers to the movement of an object in two-dimensional space, along the x and y axes. This includes both linear and rotational motion.

## 2. How is motion in a plane different from motion in a straight line?

Motion in a plane involves movement along two axes, while motion in a straight line only involves movement along one axis. In other words, motion in a plane is two-dimensional, while motion in a straight line is one-dimensional.

## 3. What is the difference between velocity and speed in motion in a plane?

Velocity refers to the rate of change of an object's position in a specific direction, while speed refers to the rate of change of an object's position regardless of direction. In other words, velocity is a vector quantity, while speed is a scalar quantity.

## 4. How are vectors used in analyzing motion in a plane?

Vectors are used to represent both the magnitude and direction of an object's motion in a plane. They can also be used to calculate the resultant velocity and acceleration of an object.

## 5. Can motion in a plane be described using equations?

Yes, motion in a plane can be described using equations such as the equations of motion, which relate velocity, acceleration, time, and displacement. These equations can also be used to solve for unknowns in a motion in a plane problem.

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