What Is the Correct Theta to Use in Calculating the Scalar Product of Vectors?

In summary, we are given vector B with a magnitude of 5.45 m and a direction angle of 60°. Vector C has the same magnitude as A and a direction angle that is 25° greater than A. We are also given that the dot product of B and A is 32.4 m2 and the dot product of B and C is 35.1 m2. Using the equation A·B=MagAxMagBcosθ, we can find the magnitude and direction of A by setting θ as the angle between the two vectors and using the given information to solve for ψ, the angle of A.
  • #1
madinsane
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Homework Statement



Let vectorB= 5.45 m at 60°. Let C have the same magnitude as A and a direction angle greater than that of A by 25°. Let B·A = 32.4 m2 and B·C = 35.1 m2. Find the magnitude and direction of A .

Homework Equations



A·B=MagAxMagBcosθ

The Attempt at a Solution


I just have one problem here. What do I use as theta? do i do cos 60?
magnitude of b is 5.45 and that of a is unknown but what about the angle?
thanks
 
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  • #2
hi madinsane! :smile:
madinsane said:
What do I use as theta? do i do cos 60?
magnitude of b is 5.45 and that of a is unknown but what about the angle?

θ is the angle between the two vectors

you'll have to give the angle of A a name, ψ say, and then the angle of C is ψ + 25° :wink:
 

FAQ: What Is the Correct Theta to Use in Calculating the Scalar Product of Vectors?

What is the definition of scalar product of vectors?

The scalar product of two vectors is a mathematical operation that produces a scalar quantity (a single number) by multiplying the magnitudes of the two vectors and the cosine of the angle between them.

How is the scalar product of vectors calculated?

The scalar product can be calculated using the dot product formula: A · B = |A| |B| cosθ, where A and B are the two vectors and θ is the angle between them. Another way to calculate it is by multiplying the corresponding components of the two vectors and then adding the products.

What is the significance of the scalar product of vectors?

The scalar product of vectors is useful in many areas of science and engineering, such as physics, mathematics, and computer graphics. It can be used to determine the angle between two vectors, find the projection of one vector onto another, and calculate the work done by a force on an object.

What is the difference between scalar product and vector product?

The scalar product produces a scalar quantity, whereas the vector product produces a vector quantity. The scalar product measures the similarity between two vectors, whereas the vector product measures the perpendicularity between two vectors.

Can the scalar product of vectors be negative?

Yes, the scalar product can be negative if the angle between the two vectors is obtuse (greater than 90 degrees). In this case, the cosine of the angle will be negative, resulting in a negative scalar product. It can also be positive or zero, depending on the angle between the two vectors.

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