# Question involving vector & magnitude

• I_noscopedJFK
In summary, the problem involves finding the smallest angle between two vectors with magnitudes of 10 and 18, and a difference of 2√10. The cosine formula, cosθ = (u dotproduct v) / (|u||v|), can be used to solve for the angle.
I_noscopedJFK

## Homework Statement

"If a vector magnitude 10 is combined with a second vector, the two vectors have a sum with a magnitude of 18 and have a difference with a magnitude of 2√10. Rounded to the nearest hundredth of a degree, what is the measure of the smallest angle between the two vectors?

## Homework Equations

cosθ = (u dotproduct v) / (|u||v|)

## The Attempt at a Solution

: |u| = 10
: |u+v| = 18
: |u-v| = 2√10

Can you tell me if I'm doing this the right way? If I am, how should I solve this?

Looks fine so far. Now square the last two equations and write the lefthand sides in terms of the dot product.

## 1. What is a vector?

A vector is a quantity that has both magnitude (size) and direction. It is represented by an arrow with a specific length and direction.

## 2. How is the magnitude of a vector calculated?

The magnitude of a vector is calculated using the Pythagorean theorem, which states that the square of the hypotenuse (longest side) of a right triangle is equal to the sum of the squares of the other two sides. In the case of a vector, the magnitude is equal to the square root of the sum of the squares of its components (x and y).

## 3. What is the difference between a scalar and a vector?

A scalar is a quantity that has only magnitude, while a vector has both magnitude and direction. Examples of scalars include temperature and mass, while examples of vectors include velocity and force.

## 4. How do you add or subtract vectors?

To add or subtract vectors, you must first break them down into their x and y components. Then, you can add or subtract the components separately to get the resulting vector. The magnitude and direction of the resulting vector can be calculated using the Pythagorean theorem and trigonometric functions.

## 5. Can a vector have a negative magnitude?

No, a vector cannot have a negative magnitude. The magnitude of a vector is always a positive value, while the direction can be positive or negative.

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