Vectors - determining ##\angle abc##

Thread starter angela107
Start date Jun 4, 2020
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Vectors

In summary, a vector is a mathematical object that represents both magnitude and direction, and is used in determining angles by representing the sides or edges of a triangle. The magnitude of a vector can be found using the Pythagorean theorem. The dot product of two vectors is a mathematical operation used to determine angles by taking the inverse cosine of the dot product divided by the product of the magnitudes of the two vectors. Vectors can be used to determine angles in three-dimensional space, but have limitations in that they can only be used in triangles or polygons with straight edges and cannot be used in non-Euclidean geometries.

Jun 4, 2020

angela107

Homework Statement: can someone see if my work is correct?

Relevant Equations: n/a

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Jun 4, 2020

member 587159

I think you made an error with calculating the vector ##\vec{BC}=[-4,0,0]##. I think you missed the minus sign here. You also want to consider ##\vec{BA}## instead of ##\vec{AB}##, so your solution checks out because two negatives cancel each other out.

Perhaps I'm misunderstanding your convention but I use ##\vec{AB}= \vec{B}- \vec{A}##.

Related to Vectors - determining ##\angle abc##

1. What is a vector?

A vector is a mathematical quantity that has both magnitude and direction. It is typically represented by an arrow, with the length of the arrow representing the magnitude and the direction of the arrow indicating the direction.

2. How do you determine the angle between two vectors?

To determine the angle between two vectors, you can use the dot product formula: ##\vec{a}\cdot\vec{b}=|\vec{a}||\vec{b}|\cos\theta##. You can rearrange this formula to solve for the angle, ##\theta##, by taking the inverse cosine of (##\vec{a}\cdot\vec{b})/(|\vec{a}||\vec{b}|)##.

3. Can you use vectors to find the angle of a triangle?

Yes, you can use vectors to find the angle of a triangle. By using the dot product formula, you can find the angle between two sides of the triangle. Then, by using the fact that the angles of a triangle add up to 180 degrees, you can find the third angle of the triangle.

4. How do you determine the direction of a vector?

The direction of a vector can be determined by finding the angle between the vector and a reference axis, such as the x-axis. This angle is typically measured counterclockwise from the reference axis. You can also use the components of the vector to determine its direction, with the x-component representing the horizontal direction and the y-component representing the vertical direction.

5. Can vectors be used in three-dimensional space?

Yes, vectors can be used in three-dimensional space. In three-dimensional space, vectors have three components: x, y, and z. The magnitude and direction of a vector can be determined using these three components. Additionally, the dot product formula can still be used to find the angle between two vectors in three-dimensional space.