How Do You Add Vectors Using Unit Vector Notation?

[1MileCrash]

Homework Statement

Consider the following vectors:

a = (5.0m) i + (2.0m) j
b = (-14m) i + (6.0m)j

Sum of a+b in unit vector notation?

Homework Equations

The Attempt at a Solution

I'm not sure about this notation, all I know about adding vectors is graphically. Does (5.0m) i + (2.0m) j mean 5 meters in direction i and 2 in direction j?

 

[lewando]

Yes, conventionally, i, j, and k are dimensionless unit vectors pointing, respectively, in the +x, +y and +z directions.

 

[1MileCrash]

Alright, got it.

Now I am asked for magnitude and direction of new vector. After adding these, I found magnitude to be 12.04 which is correct, but direction is stumping me.

I used trig to get the angle 41.64 as the angle direction of the new vector, but I'm not sure I'm finding the correct angle. After placing the vectors head to tail, I found the angle between the hypotenuse and x-axis. Is this the wrong angle?

Since it's pointing upwards and to the left, should I add 90* to my angle?

 

[lewando]

What convention are you going to use to report the angle of the resultant? A common convention is CCW from the +x axis.

 

[rwisz]

Unit vector notation is a way of representing vectors using their components in terms of unit vectors in the x, y, and z directions. In this notation, the vector a would be written as a = 5i + 2j, where i and j are unit vectors in the x and y directions, respectively. Similarly, the vector b would be written as b = -14i + 6j.

To find the sum of these two vectors in unit vector notation, we simply add their respective components together. This would give us a + b = (5i + 2j) + (-14i + 6j) = (-9i + 8j).

In words, this means that the sum of a and b is a vector with a magnitude of 9 units in the negative x direction and 8 units in the positive y direction. This notation can be useful when working with more complex vector operations and can also be used to represent vectors in three-dimensional space.