# Dot and cross product problem

• brandy
In summary, the dot product is a scalar operation on two vectors while the cross product results in a vector. When multiplying a vector with a coordinate or vector, the cross product is done first and then the dot product. This is because the cross product is only performed on vectors, while the dot product can be done on both vectors and scalars.

#### brandy

dot product and cross product. i (think dot product is like eg (1,2,4).(2,4,5) = 30 and cross product is like eg(1,2,4)x(2,4,5)=2, 8, 20) but I am not sure... and is there an order like in a.bxc do u do bxc and then.a or do u go normal left to right. but if left to right what's the rule in when u multiply one number by a coordinante or vector...

brandy said:
and is there an order like in a.bxc do u do bxc and then.a or do u go normal left to right.

A dot product operation on two vectors results in a scalar i.e. a number [not a vector]. Whereas, the cross product always results in a vector. As for a.(b x c), you CANNOT open the bracket as: (a.b x a.c). This is because cross product is operation that is done on vectors and not on scalars, whereas both, a.b and a.c are scalars.

So, you have to first find out the cross product of b & c, and then solve for the dot product of the resultant vector and a to get your answer.

thanks for clearing that up

## 1. What is the difference between dot and cross product?

The dot product, also known as the scalar product, is a mathematical operation between two vectors that results in a scalar quantity. It is calculated by multiplying the magnitudes of the two vectors and the cosine of the angle between them. On the other hand, the cross product, also known as the vector product, results in a vector quantity and is calculated by multiplying the magnitudes of the two vectors and the sine of the angle between them.

## 2. In what situations would you use the dot product?

The dot product is commonly used in physics and engineering to calculate work, energy, and projections of one vector onto another. It is also used in geometry to determine angles and distances between vectors.

## 3. What is the geometric interpretation of the cross product?

The geometric interpretation of the cross product is that it results in a vector that is perpendicular to both of the original vectors being multiplied. The magnitude of the cross product is equal to the area of the parallelogram formed by the two original vectors.

## 4. How do you calculate the dot and cross product of two vectors?

To calculate the dot product, you multiply the x components of the two vectors, then the y components, and finally the z components. Then, you add these products together. To calculate the cross product, you use the formula: (u1v2 - u2v1)i + (u2v3 - u3v2)j + (u3v1 - u1v3)k, where u and v are the two vectors being multiplied and i, j, and k are the unit vectors in the x, y, and z directions respectively.

## 5. What is the significance of the dot and cross product in vector algebra?

The dot and cross product are essential operations in vector algebra as they allow us to perform calculations involving vectors such as finding angles, projections, and determining perpendicularity. They also have applications in physics, engineering, and computer graphics. Additionally, they help us understand the relationship between vectors and geometric concepts such as area and volume.