Find the Magnitude and the Direction (Unit Vetors)

• sugar1
In summary, the conversation is about a student who missed their physics class and needs help understanding questions about adding and subtracting unit vectors and calculating their magnitudes and directions. They also request a diagram for clarification. The conversation ends with a suggestion to use component notation to solve the given equations.
sugar1
Hi,

I missed the first lecture of my physics class and need help answering these simple questions. They have to do with adding and subtraction and multiplying unit vectiors. What do they mean by direction, this is in degrees?

Also, I am not sure if this is possible but a diagram would be very helpful.

Homework Statement

Suppose B = -7i + 2j and G=6i - 4j. Find the magnitude and direction of:

a.) B + G
b.) B - G
c.) 3B

Thank you

Do you have a textbook for your class? It will show you how to add and subtract vectors, calculate their magnitudes, and find unit vectors.

sugar1 said:
Hi,

I missed the first lecture of my physics class and need help answering these simple questions. They have to do with adding and subtraction and multiplying unit vectiors. What do they mean by direction, this is in degrees?

Also, I am not sure if this is possible but a diagram would be very helpful.

Homework Statement

Suppose B = -7i + 2j and G=6i - 4j. Find the magnitude and direction of:

a.) B + G
b.) B - G
c.) 3B

Thank you
Can you determine at least what B+ G, B- G, and 3B are? The point of "component notation" is that you can deal with the corresponding components separately:
(ai+ bj)+ (ci+ dj)= (a+c)i+ (b+d)j, 3(ai+ bj)= 3ai+ 3bj.

1. What is the difference between magnitude and direction in vector quantities?

The magnitude of a vector is its size or length, while the direction refers to the angle at which the vector points. Magnitude is a scalar quantity, meaning it only has a numerical value, whereas direction is a vector quantity since it has both magnitude and direction.

2. How do you find the magnitude of a vector?

To find the magnitude of a vector, you can use the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In other words, the magnitude is the square root of the sum of the squares of the vector's components.

3. What are unit vectors and how are they used?

Unit vectors are vectors with a magnitude of 1 and are typically used to represent the direction of a vector. They are useful because they do not change the magnitude of a vector when multiplied by a scalar. Unit vectors are also used to represent the basis vectors of a coordinate system.

4. How do you represent the direction of a vector using unit vectors?

To represent the direction of a vector using unit vectors, you can break the vector into its x, y, and z components and then multiply each component by its respective unit vector (i, j, k for x, y, z). The resulting sum will be a unit vector pointing in the same direction as the original vector.

5. Can the magnitude of a vector be negative?

No, the magnitude of a vector is always a positive value. It represents the size or length of the vector and cannot be negative. However, the direction of a vector can be positive or negative, depending on the angle at which it points.

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