For the three vectors shown above in the figure, A⃗ +B⃗ +C⃗ =− 1.60 i^. What is vector B⃗ ? What is the magnitude of B⃗ ? How many degrees above the negative x-axis does B⃗ point?

Question

For the three vectors shown above in the figure, A⃗ +B⃗ +C⃗ =− 1.60 i^. What is vector B⃗ ? What is the magnitude of B⃗ ? How many degrees above the negative x-axis does B⃗  point?

mony01 · Answer

attachment

aum · Answer

What is vector A from the diagram?
What is vector C from the diagram?

mony01 · Answer

A is 4 and C is 2

aum · Answer

A + B + C = -1.60i
B = -1.60i - A - C   ------ (1)

From the diagram:
A = 4i ;  C = -2j   Substitute in equation (1)

B = -1.60i - 4i + 2j 
B = -5.6i + 2j

$|B| = \sqrt{(-5.6)^2 + 2^2} = \sqrt{31.36+4} = \sqrt{35.36} = 5.95$
$|\tan(\theta)| = 2/5.6$.  Find $\theta$.