How Is the Angle Between Two Vectors Determined Using Their Dot Product?

In summary, the dot product with angle, also known as the scalar product, is a mathematical operation used to measure the similarity or alignment between two vectors. It is calculated by multiplying the corresponding components of the vectors and adding the results. The angle in the dot product is significant as it determines the degree of alignment between the vectors. The dot product with angle has various applications in physics, engineering, and computer graphics. It can also be negative, indicating a lower degree of alignment or opposite directions of the two vectors.
  • #1
StephenDoty
265
0
One vector has a length of 23 units and another a length of 12 units. If the scalar product of these two vectors is 113, what is the angle between the two vectors?

A dot B = ABcos(theta)
113 = 12*23*cos(theta)
113/276= cos(theta)
cos^(-1)113/276 = theta
65.8 degrees or 66 degrees using sig figs = theta

is this right?
 
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  • #2
yes yes
 
  • #3
easy.
 

1. What is the dot product with angle?

The dot product with angle, also known as the scalar product, is a mathematical operation that takes two vectors as inputs and returns a single number as output. It is used to calculate the degree of similarity or alignment between two vectors.

2. How is the dot product with angle calculated?

The dot product with angle is calculated by multiplying the corresponding components of two vectors and adding the results. In other words, it is the sum of the products of each pair of components in the vectors.

3. What is the significance of the angle in the dot product?

The angle in the dot product is important because it determines the degree of similarity or alignment between the two vectors. A smaller angle indicates a higher degree of alignment, while a larger angle indicates a lower degree of alignment.

4. What are the applications of the dot product with angle?

The dot product with angle has various applications in fields such as physics, engineering, and computer graphics. It is used to calculate work and energy in physics, determine the direction of forces in mechanics, and perform transformations in computer graphics.

5. Can the dot product with angle be negative?

Yes, the dot product with angle can be negative. This occurs when the angle between the two vectors is greater than 90 degrees, indicating a lower degree of alignment. A negative dot product can also indicate that the two vectors are pointing in opposite directions.

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