# Solving for Vector Expression: 12.0 m and 170° (i+j)

• chocolatelover
In summary, to find an expression in component form for a vector with magnitude 12.0 m and direction 170°, you can use the equations Ax=12cos170 and Ay=12sin170. However, it is important to consider the quadrant the angle falls in to determine the correct signs for the components.
chocolatelover

## Homework Statement

Find an expression in component form for 12.0 m and 170° (i+j)

Ax=Acostheta
Ay=Asintheta

## The Attempt at a Solution

I was thinking about using one of these equations, but I don't know which one to use or if there is another way of doing it. Does it matter which one I use?

Would it be

12.0cos170? but I don't know where the i or the j would go

Could someone please show me how to set this problem up?

Thank you very much

Yes, it matters which one you use for a particular component. Why not draw the vector on a graph? To break it up into its components: the x component (i) is the first equation you've written down, the y (j) component is the second one. You can prove this to yourself by using the graph and some trigonometry.

As an additional check, you can go back from i and j to polar notion. The magnitude is essentially what I told you in the other thread i.e. |A|. The angle is tan^-1 (y/x) (thats the inverse tangent)

EDIT: An important note about evaluating tan^-1() using a calculator. If your components are in quadrants one and four, your answer in degrees is correct. However if your components are in the second and third quadrants, your answer is off by 180 degrees. Therefore you have to add or subtract 180 degrees from the answer tan^-1() gives you. It does not matter if you add or subtract, as they are both correct. Your problem is a classic example of this. Try it!

Last edited:
i is usually the x direction
j is usually the y direction
draw a diagram, and see the projection onto the x and y axes to visualise, then use trig to determine which equation to use.

Thank you very much

Does 12sin10 look right for the i (x component)?

Thank you

Last edited:
Can someone please tell me if this is correct?

Thank you

chocolatelover said:
Thank you very much

Does 12sin10 look right for the i (x component)?

Thank you

one thing is unclear here... is the angle measuring from the positive x-axis?
draw a diagram if unsure what is what.

Thank you

is the angle measuring from the positive x-axis?

Yes. Would i be 12cos10 and would j be 12sin10? Would I use 10°? (180-170)

Thank you

Last edited:
chocolatelover said:
Yes. Would i be 12cos10 and would j be 12sin10? Would I use 10°? (180-170)

Yes, just be careful. 170° is in the 2nd quadrant, so your 'x' or 'i' value will be negative. So, it's actually -(12cos10).

Thank you very much

Regards

## What is a vector expression?

A vector expression is a mathematical representation of a vector, which includes both magnitude and direction. It is typically written in the form of a magnitude m and an angle θ, such as 12.0 m and 170° in this example.

## How do you solve for a vector expression?

To solve for a vector expression, you can break it down into its horizontal and vertical components using trigonometry. In this example, a is the magnitude, which is 12.0 m, and θ is the angle, which is 170°. You can then use the formula x = acosθ and y = asinθ to find the horizontal and vertical components of the vector.

## Why is it important to solve for vector expressions?

Solving for vector expressions is important because it allows us to understand and manipulate the direction and magnitude of a vector. This is useful in many scientific fields, such as physics and engineering, where vectors play a crucial role in understanding and predicting the behavior of objects.

## What is the difference between magnitude and direction in a vector expression?

Magnitude refers to the size or length of a vector, while direction refers to the angle or orientation of the vector. In the example of 12.0 m and 170°, 12.0 m is the magnitude and 170° is the direction.

## Can vector expressions be represented graphically?

Yes, vector expressions can be represented graphically using arrows. The length of the arrow represents the magnitude of the vector and the direction of the arrow represents the direction of the vector. In this example, the arrow would be 12.0 units long and pointing in the direction of 170° on a coordinate plane.

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