Calculate the Angle (a + b) Makes with the x-axis for Vector (a + b)

[imy786]

Homework Statement

if vector :

line a starts from co-ordinates (0,0) and ends at (5,3)

line b starts from co-ordinates (0,0) and ends at (1,2)

what angle to the x-axis does the vector (a + b) make?

Homework Equations

tan ∅ = opposite / adjacent

The Attempt at a Solution

we can work out what angle a makes then what angle b makes.

then subtract angle b from a.

tan a = opposite / adjacent
tan a ^-1 (3/5) = a=30.964

tab b ^ (2/1) =b=63.435

b-a = 63.435-30.964
= 32.47 degrees

is this correct?

 

[gb7nash]

No. You want to add the vectors first, then take the angle. What is the x component of a+b? What is the y component of a+b? Once you have these, then you can use the angle formula.

 

[imy786]

(5,3) + (1,2) = (6,5) is the vector of (a+b)

tan a = opposite / adjacent
tan a ^-1 (5/6) = a=39.806 degrees

tan x ^-1 (3/5) = x=30.964

angle of (a+b) = 8.842 degrees

is this correct

 

[gb7nash]

(5,3) + (1,2) = (6,5) is the vector of (a+b)

This is fine. I'm not quite sure why you're still subtracting angles though.

tan(angle of a+b) = opposite/adjacent = ...

What's opposite? adjacent?

 

[imy786]

tan a = opposite / adjacent
tan a ^-1 (5/6) = a=39.806 degrees

 

[gb7nash]

tan a = opposite / adjacent
tan a ^-1 (5/6) = a=39.806 degrees

This is the correct answer. Minor technicality though. You're taking the tangent of the angle of a+b, not the tangent of a.

 

[imy786]

tan ( a + B ) = opposite / adjacent
tan (a+b) ^-1 (5/6) =

angle of (a + b)=39.806 degrees

Thanks gb7nash

 

[Mark44]

tan (a+b) ^-1 (5/6) =

I have no idea what you mean by this.

 

[gb7nash]

I have no idea what you mean by this.

Good catch, I didn't even notice that.