PLEASE HELP WITH PART E AND F THANKS!!
Find the direction and magnitude of the following vectors.
A⃗ =( 22 m )x^+( -15 m )y^
Express your answer in degrees using three significant figures.
θA =
THE ANSWER IS-34
Part B
Express your answer in meters using two significant figures.
|A⃗ | = m THE ANSWER IS 27M
Part C
B⃗ =( 2.5 m )x^+( 16 m )y^
Express your answer in meters using two significant figures.
θB = THE ANSWER 81 DEGREE
Part D
Express your answer in meters using two significant figures.
|B⃗ | = m THE ANSWER 16 M
Part E
A⃗ +B⃗
Express your answer in degrees using three significant figures.
θA⃗ +B⃗ =
Part F
Express your answer in meters using two significant figures.
|A⃗ +B⃗ | = m
To find the direction and magnitude of vectors, we can use trigonometry and the Pythagorean theorem.
Part E:
To find the direction of the vector A⃗ + B⃗, we can add the x-components and y-components of both vectors separately.
A⃗ + B⃗ = (22 m)x^ - (15 m)y^ + (2.5 m)x^ + (16 m)y^
Combining like terms:
A⃗ + B⃗ = (22 m + 2.5 m)x^ + (-15 m + 16 m)y^
A⃗ + B⃗ = (24.5 m)x^ + (1 m)y^
Now, we can find the direction of the vector A⃗ + B⃗ using the formula:
θ = tan^(-1)(y-component / x-component)
θA⃗ + B⃗ = tan^(-1)(1 m / 24.5 m)
Using a calculator, θA⃗ + B⃗ is approximately equal to 2.3 degrees.
Part F:
To find the magnitude of the vector A⃗ + B⃗ , we can use the Pythagorean theorem.
|A⃗ + B⃗ | = √((x-component)^2 + (y-component)^2)
|A⃗ + B⃗ | = √((24.5 m)^2 + (1 m)^2)
Using a calculator, |A⃗ + B⃗ | is approximately equal to 24.5 meters.