Unknown angle between two vectors

The vector product of two vectors AB can be represented as AB = |AB|sin(θ), where |AB| is the magnitude of AB and θ is the angle between the two vectors. Therefore, in this case, the magnitude of AB is 9. In summary, the scalar product of vectors AB is -6 and the vector product of AB is 9. To find the angle between vectors A and B, we can use the fact that the scalar product is equal to the cosine of the angle between the vectors and the vector product is equal to the sine of the angle between the vectors. By setting these equations equal to each other and using trigonometric identities, we can find that the angle between the vectors is -56
  • #1
student34
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Homework Statement


Scalar product of vectors AB = -6; vector product of AB = 9. Find the angle between vectors A and B.


Homework Equations


Scalar product: cos(θ)*AB
Vector product: sin(θ)*AB
(sin(θ))/cos(θ) = tanθ

The Attempt at a Solution


AB = -6/cos(θ)
AB = 9/sin(θ)
9/sin(θ) = -6/cos(θ)
9/-6 = (sin(θ))/cos(θ)
3/-2 = tan(θ)
tan^-1(3/-2) = -56° which I take to mean 56° from each other.
But their answer is 124° which is -56° + 180°. How can this be when the whole time we are dealing with one angle between two vectors?
 
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  • #2
student34 said:
3/-2 = tan(θ)

tan θ = negative value means θ can only be 90<θ<180 or 270<θ<360.


I have a question also , why the vector product which is a vector can equal to 9? is that a magnitude of AxB?
Thank you
 
  • #3
Outrageous said:
tan θ = negative value means θ can only be 90<θ<180 or 270<θ<360.

Ohhhh, I see, thanks.

I have a question also , why the vector product which is a vector can equal to 9? is that a magnitude of AxB?
Thank you

Yes, I should have mentioned that.
 

FAQ: Unknown angle between two vectors

1. What is an unknown angle between two vectors?

An unknown angle between two vectors is the angle formed by two vectors when their initial points are placed at the same point. It is the angle between the two vectors, measured in degrees or radians, that determines their direction and magnitude relative to each other.

2. How is the unknown angle between two vectors calculated?

The unknown angle between two vectors can be calculated using the dot product formula: θ = cos^-1 (a · b / |a||b|), where a and b are the two vectors and |a| and |b| represent their magnitudes. This formula gives the angle in radians. To convert to degrees, multiply the result by 180/π.

3. What is the significance of the unknown angle between two vectors in physics?

In physics, the unknown angle between two vectors is important in determining the direction and magnitude of forces acting on an object. It can also be used to calculate the work done by a force, as well as the torque and angular momentum in rotational motion.

4. Can the unknown angle between two vectors be negative?

Yes, the unknown angle between two vectors can be negative. This occurs when the vectors are pointing in opposite directions, and the angle between them is greater than 180 degrees. The negative sign indicates that the angle is measured in the opposite direction.

5. How does the unknown angle between two vectors change when one vector is multiplied by a scalar?

Multiplying one vector by a scalar does not change the unknown angle between the two vectors. This is because scalar multiplication only changes the magnitude of the vector, not its direction. Therefore, the angle between the two vectors remains the same.

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