# Finding angle through cross and dot product

• cxiangzhi
In summary, the conversation discussed how the use of both cross and dot products can help find the angle between two vectors. However, the speaker encountered an issue where the results of the two products did not match. They provided the vectors used and the results obtained through dot and cross products. The speaker also mentioned using the determinant method to solve the cross product. It was then pointed out that the cross product alone cannot distinguish between certain angles. The speaker also asked for clarification on the meaning of "per se," which was explained as a Latin phrase meaning "in itself."
cxiangzhi
By using both cross and dot products, the angle between 2 vectors can be found. But there is 1 question that I tried for countless times that the result of cross product and dot product are not the same.

Here is the vectors that I am talking about

A= 2i+3j=k
B= -4i+2j-k

The result by using dot product = 100.08°
The result by using cross product = 79.92°

What is 2i+3j=k?

My mistake. Its A= 2i+3j+k

AxB=-5i-2j+16k

abs(AxB) = 16.88

abs(AxB)=abs(A) x abs(B)sinθ

∴ abs(AxB)/(abs(A) x abs(B))= sinθ
∴ θ = 79.92

A.B=-3

A.B/(abs(A) x abs(B))= cos(theta)

∴θ = 100.08

The result of dot and cross product should be the same but its not in this case. Please help.

Last edited:
Are you using matrices to solve the cross product?

Yeap.. I used the determinant method to solve the cross product..

Observe that sin 79.92 = sin 100.08. So the cross product per se cannot distinguish between such angles.

Im sorry but I still have a question here.. What is per se?

Thanks a lot guys.. Appreciate you help.. :)

## 1. What is the cross product and how is it used to find angles?

The cross product is a mathematical operation that takes two vectors as input and outputs a third vector that is perpendicular to both of the input vectors. It is denoted by the symbol "x". The magnitude of the cross product of two vectors is equal to the product of the magnitudes of the two vectors times the sine of the angle between them. Therefore, by using the cross product, we can find the angle between two vectors.

## 2. How does the dot product help in finding angles between vectors?

The dot product is another mathematical operation that takes two vectors as input and outputs a scalar value. The dot product of two vectors is equal to the product of the magnitudes of the two vectors times the cosine of the angle between them. Therefore, by using the dot product, we can find the angle between two vectors.

## 3. Can the cross product and dot product be used interchangeably to find angles?

No, the cross product and dot product cannot be used interchangeably to find angles. While both operations involve finding the angle between two vectors, they use different mathematical formulas and have different outputs. The cross product outputs a vector, while the dot product outputs a scalar value.

## 4. What is the difference between using the cross product and dot product to find angles?

The main difference between using the cross product and dot product to find angles is the type of output they provide. The cross product outputs a vector, which can be used to determine the direction of the resulting vector, while the dot product outputs a scalar value, which only provides information about the magnitude of the resulting vector. Additionally, the cross product requires the use of the sine function, while the dot product requires the use of the cosine function.

## 5. Are there any limitations to using the cross product and dot product to find angles?

Yes, there are limitations to using the cross product and dot product to find angles. These operations can only be used to find the angle between two vectors that are in three-dimensional space. They also assume that the vectors are in the same plane and have a common starting point. If these conditions are not met, the results may not accurately represent the angle between the two vectors.

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