Question

Find vectors having (a) | ⃗| = 3 and 270°
with negative x-axis. (b) | ⃗⃗| = 10 and 90° with positive y-axis​

Answer 1

Answer:

Vector A has a magnitude of 10 units and makes an angle of 30° with the positive x-axis. Vector B has a magnitude of 20 units and makes an angle of 30° with the negative x- axis. What is the magnitude of the resultant between these two vectors?

The resultant of the given two vectors can easily be figured out just by resolving the vectors into x and y components

Resolving A vector, we get 10cos(30°) and 10sin(30°) , which is equal to 5√3 and 5 along x and y axis respectively

Now resolving B vector, we get -20cos(30°)[carries negative sign as it is along negative X-axis] and 20sin(30°), which is equal to -10√3 and 10 along X and Y axis respectively

Equating the resolved vectors that are along x axis, we get -5√3 ,which can be assigned to Rx (just for our convenience)

Equating the resolved vectors that are along Y axis, we get 15,which can be taken as Ry

Thus the X and Y components of the resultant vector has been found out

Futher Pythagoras theorem can be used to calculate the resultant vector ‘R’ using its X and Y components ( i.e Rx and Ry)

Therefore ‘R’ vector =√(Rx^2 + Ry^2)

=√(5√3^2 + 15^2) = √(225+75) = √300

=10√3 = 17.32

The magnitude of the resultant vector is 17.32

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