If the length and amplitude of 2 different vectors are given to you, how do I find the sum of the two?

Question

I need to find the magnitude and amplitude of the resultant. My teacher showed us a way to do it without having to draw them...but I don't understand.

for example...vector A is 60 degrees and 27mm long. Vector B is 135 degrees and 15mm long. what would the magnitude and amplitude of Vector A + Vector B equal?

Answer 1

"for example...vector A is 60 degrees and 27mm long. Vector B is 135 degrees and 15mm long. what would the magnitude and amplitude of Vector A + Vector B equal?"

x-direction: vx = 27cos 60 + 15 cos 135
y-direction: vy = 27sin 60 + 15 sin 135

Magnitute: √(vx^2+vy^2) mm
New direction: ∅ = arctan vy/vx degree

Answer 2

for example...vector A is 60 degrees and 27mm long. Vector B is 135 degrees and 15mm long. what would the magnitude and amplitude of Vector A + Vector B equal?

A: The x component is 27 sin 60 & the y component is 27 cos 60

B: The x component is 15 sin 135 & the y component is 15 cos 135

A+B=(27*sin 60+15sin 135)x+(27cos 60+15 cos 135)y
A+B=33.989x+2.893y

magnitude=√(33.989^2+2.893^2)=34.112 mm

direction=arctan (33.989/2.893)=85.135°

Answer 3

What do you mean by 'amplitude'? Vectors can be expressed either by their compontents, or equivalently, their length (or magnitude) and direction.

Vector additon is defined as adding the components so you have to put both vectors in component form before you can do so.

Answer 4

Using a basic example:

let one vector be A, the other be B.

then you assign each like this:

A = a(1)i + a(2)j + a(3)k

B = b(1) + b(2)j + b(3)k

where a(1) equals the number in front of i, a(2) equals the number in front of j, etc. and same for b.

the sum of A and B is:

A + B = (a1 + b1)i + (a2 + b2)j + (a3 + b3)k

Answer 5

You would use normal right angle trigonemetry if the angle is 90 degrees. Or sine and cosine laws if the angles are 135 degrees, ect.

Answer 6

length = amplitude
You need to know the direction of each vector.
Use the parallelogram construction for the sum.

Th

Answer 7

sahsjing and mu_do_in both have the right idea, but mu_do_in got sin and cos reversed. So do it the way sahsjing suggests.