Vector Addition: Solving for C→ in A→+B→+C→=0

Thread starter negation
Start date Jan 17, 2014
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Vector

In summary, vector addition is a mathematical operation used to combine two or more vectors into a new vector. It is commonly used to represent multiple forces acting on an object. To solve for C→ in A→+B→+C→=0, one must subtract A→ and B→ from both sides of the equation. If C→=0, this means the object is at rest and the net force is equal to zero. In order to solve for C→, all three vectors (A→, B→, and C→) must be given. Vector addition has practical applications in physics, engineering, and navigation to calculate net force, design structures, and determine an object's movement.

Jan 17, 2014

negation

Homework Statement

Let A→ = 15i -40j and B→ = 31j + 18k. Find C→ such that A→+B→+C→=0

The Attempt at a Solution

A + B = 15i - 9j + 18k

C = -15i + 9j -18k

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Jan 17, 2014

CWatters

Science Advisor

Homework Helper

Gold Member

Looks correct to me.

1. What is vector addition?

Vector addition is a mathematical operation that involves combining two or more vectors to create a new vector. It is used to represent the combination of multiple forces acting on an object.

2. How do you solve for C→ in A→+B→+C→=0?

To solve for C→, you need to rearrange the equation to isolate C→ on one side. This can be done by subtracting A→ and B→ from both sides of the equation, resulting in C→=-A→-B→. This means that C→ is equal in magnitude and direction to the negative sum of A→ and B→.

3. What does it mean when C→=0 in vector addition?

If C→=0, this means that the three vectors A→, B→, and C→ are in equilibrium. This can also be interpreted as the object being at rest, as the net force acting on it is equal to zero.

4. Can you solve for C→ in A→+B→+C→=0 if only two vectors are given?

No, in order to solve for C→, you need to have all three vectors (A→, B→, and C→) given. This is because the equation represents the vector sum of all three vectors, and without one of the vectors, you cannot accurately determine the magnitude and direction of C→.

5. How is vector addition used in real-life applications?

Vector addition is used in various fields such as physics, engineering, and navigation. It is used to calculate the net force acting on an object, design structures that can withstand multiple forces, and determine the direction and speed of an object's movement.