# Two vectors have magnitudes of 10 and 15

• nath_quam
In summary, the conversation is about a question involving two vectors with magnitudes of 10 and 15, an angle of 65 degrees between them and finding the component of the longer vector along a line perpendicular to the shorter vector. The possible options for the component length are 0, 4.2, 9.1, 13.6, and 6.3. The person asking for help is asked to show their attempt at a solution and the conversation is moved to the homework forum. The solution involves drawing a picture and using a trigonometric function to find the desired length.

#### nath_quam

Hey I'm just having trouble with this question

Two vectors have magnitudes of 10 and 15. The angle between them when they are drawn with their tails at the same point is 65 deg. The component of the longer vector along the line perpendicular to the shorter vector, in the plane of the vectors, is:

a)0
b)4.2
c)9.1
d)13.6
e)6.3

Thanks Nath

Show your attempt at a solution if this is a homework problem.

In fact, I am moving this to the homework forum.

Draw a picture of the situation. Do you see a right triangle? What trig function will help you find the length you want?

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## 1. What is the magnitude of the resultant vector when two vectors have magnitudes of 10 and 15?

The magnitude of the resultant vector is the length or size of the vector that results from adding the two given vectors together. In this case, the magnitude of the resultant vector would be √(10^2 + 15^2) = √(100 + 225) = √325 ≈ 18.03.

## 2. What is the direction of the resultant vector when two vectors have magnitudes of 10 and 15?

The direction of the resultant vector can be found using trigonometry. The angle between the two vectors can be calculated using the inverse tangent function (tan^-1) with the formula θ = tan^-1 (15/10) = 56.31 degrees. Therefore, the resultant vector has a magnitude of 18.03 and a direction of 56.31 degrees.

## 3. How do you find the magnitude of the individual components of the resultant vector?

The individual components of the resultant vector can be found using basic trigonometric functions. The horizontal component, or x-component, can be found using the formula R cos θ, where R is the magnitude of the resultant vector and θ is the angle between the resultant vector and the x-axis. Similarly, the vertical component, or y-component, can be found using the formula R sin θ. In this case, the x-component would be 18.03 cos 56.31 ≈ 11.29 and the y-component would be 18.03 sin 56.31 ≈ 14.36.

## 4. Can the magnitudes of the two vectors be negative?

No, magnitudes cannot be negative. Magnitude refers to the size or length of a vector, which is always a positive value. Negative values can only represent the direction of a vector.

## 5. What is the difference between the magnitude and direction of a vector?

The magnitude of a vector refers to its size or length, while the direction of a vector refers to the angle or orientation of the vector in relation to a reference axis. In other words, magnitude and direction are two different properties that describe a vector.