# Representing Vectors in 3D Space

• Tiven white
In summary, the conversation is about representing a full vector in 3D space and identifying which of the given options is not a valid way to do so. The options include representing the vector in Cartesian form, as a magnitude times a unit vector, as a Cartesian vector times a unit vector, or as a magnitude with coordinate angles. The individual trying to solve the problem has found all options except one to be potentially correct and is seeking clarification on which option is incorrect. They also consider the possibility of using vector multiplication, such as the dot product, to determine the correct answer.
Tiven white

## Homework Statement

In 3D space a full vector can be represented I. All the following except
A. In Cartesian vector form
B.As a magnitude times a unit vector
C. As a Cartesian vector times a unit vector
D. As magnitude with coordinate angles

## The Attempt at a Solution

I say the answer is reason being I found all the other statements correct therefore I solve by elimination of variables. Any help would be g greatly appreciated and verification for my answer.

Tiven white said:

## Homework Statement

In 3D space a full vector can be represented I. All the following except
A. In Cartesian vector form
B.As a magnitude times a unit vector
C. As a Cartesian vector times a unit vector
D. As magnitude with coordinate angles

## The Attempt at a Solution

I say the answer is reason being I found all the other statements correct therefore I solve by elimination of variables. Any help would be g greatly appreciated and verification for my answer.

What does a vector times a vector mean? Think about that.

Dick said:
What does a vector times a vector mean? Think about that.

Is the answer c due to the fact that the vector times a vector can produce a scalar

Tiven white said:
Is the answer c due to the fact that the vector times a vector can produce a scalar

Depends on what the problem means by 'times'. If the only product you know about is the dot product, then yes, answer c is certainly a candidate for elimination.

Your answer is correct. In 3D space, vectors can be represented in Cartesian vector form (x,y,z), as a magnitude (length) multiplied by a unit vector (direction), or as a combination of both (Cartesian vector multiplied by a unit vector). Using coordinate angles to represent a vector is not a common method and is not typically used in 3D space. So the correct answer is A. In Cartesian vector form.

## 1. How are vectors represented in 3D space?

In 3D space, vectors are typically represented by a directed line segment with a starting and ending point. They can also be represented by a column or row matrix containing the values for the vector's direction and magnitude.

## 2. What is the difference between a position vector and a free vector?

A position vector represents a specific point in 3D space, while a free vector represents a direction and magnitude without a specific starting point. Position vectors are typically used for navigation and positioning, while free vectors are used for calculations and analysis.

## 3. How are vectors added in 3D space?

To add vectors in 3D space, you can use the head-to-tail method or the parallelogram method. In the head-to-tail method, you place the tail of one vector at the head of another and draw a line from the tail of the first vector to the head of the second. The resulting vector is the sum of the two original vectors. In the parallelogram method, you draw the two vectors from a common starting point and create a parallelogram. The resulting vector is the diagonal of the parallelogram.

## 4. Can vectors in 3D space be multiplied?

Yes, vectors in 3D space can be multiplied by a scalar (a single value). This results in a new vector with the same direction as the original vector, but with a magnitude that is multiplied by the scalar value. This is known as scalar multiplication.

## 5. What is the dot product of two vectors in 3D space?

The dot product of two vectors in 3D space is a scalar value that represents the magnitude of the projection of one vector onto the other. It is calculated by multiplying the corresponding components of the two vectors and then adding them together. The dot product is useful for calculating the angle between two vectors and for determining if two vectors are perpendicular.

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