# Magnitude of vector CD?

• erpoi
In summary, to find the magnitude of vector CD, which is the vector from point C to point D, we can use the cosine rule on the triangle formed by points C, D, and the origin. We know that the magnitude of vector c is 5, the magnitude of vector d is 7, and the dot product of c and d is 4. By using the cosine rule, we can find the value of cos(\theta) to be \frac{4}{35}. This gives us an exact value of magnitude of vector CD to be \sqrt{66}.

#### erpoi

C, D are points defined by position vectors c and d. Magnitude of c is 5, mag of d is 7, c dotproduct d is 4 ie c.d = 4, find the magnitude of vector CD.

So i started this way

c.d = magc*magdcos@
= 35cos@, @ = 83.4 degrees

But still no idea how do get magnitude of vector cd. Thank you!

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Are you sure it isn't the magnitude of vector CD? (i.e. the vector from point C to point D)? If so, use the cosine rule on the triangle, since you know two vectors and an angle.

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oops yes you are right, ok i use the cos rule and do get an answer(which is correct), but I am after it as an exact value (root66). How would i get that? Thanks!

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?? You say you got an answer but you want an exact value? Did you use a calculator to get $cos(\theta)$. Since you want to use $cos(\theta)$ in the cosine rule, why not just use $cos(\theta)= \frac{4}{35}$ rather than finding $\theta$ itself?

## 1. What is the magnitude of vector CD?

The magnitude of a vector is the length or size of the vector, which is represented by a number. In the case of vector CD, the magnitude refers to the distance from the starting point (C) to the endpoint (D) of the vector. It is denoted by ||CD|| or |CD|.

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

The magnitude of vector CD can be calculated using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (longest side) is equal to the sum of the squares of the other two sides. In this case, the magnitude of vector CD equals the square root of the sum of the squares of the horizontal and vertical components of the vector.

## 3. Can the magnitude of vector CD be negative?

No, the magnitude of a vector is always a positive number. It represents the absolute value or distance of the vector and does not take into account its direction. However, the vector itself can be negative if it is pointing in the opposite direction.

## 4. What are the units of measurement for the magnitude of vector CD?

The units of measurement for the magnitude of vector CD will depend on the units used for the coordinates or components of the vector. For example, if the coordinates are given in meters, the magnitude will also be in meters. It is important to include the units when stating the magnitude of a vector to provide context and clarity.

## 5. Does the magnitude of vector CD change if the coordinates are changed?

Yes, the magnitude of a vector is dependent on the coordinates or components of the vector. If the coordinates are changed, the magnitude will also change. However, the direction of the vector will remain the same as long as the angle between the vector and the positive x-axis remains constant.