Question

Evaluate the following expression: -1(5,-1) + 2(1,1)..

Evaluate the following expression: 2(1,1) - 4(0,1). Enter your answer as a vector.

Answer 1

I could be wrong, but I assume you multiply out the -1 and positive 2 in the first case:

-1(5, -1)+2(1,1)=s
becomes..
(-5, 1) + (2, 2)=s
Add x with x and y with y...

(-3, 3)=s

The answer is wanted as a vector, therefore..

Mag(s)=sqrt((-3)^2+(3)^2)=3
The angle can be found by tan, knowing that S is in the second quadrant:

theta_s=tan^-1(-3/3)=-45

HOWEVER, it is in the second quadrant, so the angle from the positive x axis would be 135.

In vector form, your answer would be a vector of magnitude 3, and angle 135. This can be written in vector form:

s=r(cos(theta)+isin(theta)
s=3(cos(135)+isin(135))

I could be wrong... :\

Answer 2

I already found a mistake, the magnitude isnt 3..

Sqrt(3^2+3^2) isnt 3, isnt sqrt(18) which is 4.24..

Sorry