Question

Vector a has magnitude of 13.5 and is 345o counter-clockwise up from the x-axis. what are the x- and y-components of the vector

Answer 1

The x and y components of vector a are 13.04units and -3.49units respectively.

Step-by-step explanation:

Given a vector say m, the x component of m (
`m_(x)`) is given by;

`m_(x)` = |m| cos θ

and the y-component (
`m_(y)`) is given by;

`m_(y)` = |m| sin θ

Where;

|m| = magnitude of vector m

θ = the angle that vector m makes with the x-axis (counterclockwise)

Now, given;

Vector a

Magnitude of a (written as |a|) = 13.5 units

direction = 345° counterclockwise

The x component of vector a (
`a_(x)` ) is given by;

`a_(x)` = |a| cos θ

Where;

|a| = 13.5

θ = 345° counterclockwise

=>
`a_(x)` = 13.5 cos 345°

=>
`a_(x)` = 13.5 x 0.9659

=>
`a_(x)` = 13.04 units

Similarly, the y component of vector a (
`a_(y)` ) is given by;

`a_(y)` = |a| sin θ

Where;

|a| = 13.5

θ = 345° counterclockwise

=>
`a_(y)` = 13.5 sin 345°

=>
`a_(y)` = 13.5 x -0.2588

=>
`a_(y)` = - 3.49 units

Therefore, the x and y components of vector a are 13.04units and -3.49units respectively.

Answer 2

x-component of a vector = (magnitude) · cos( Θ )

x-component = (13.5) · cos(345°) = (13.5) · (0.966) = 13.04

y-component of a vector = (magnitude) · sin( Θ )

y-component = (13.5) · sin(345°) = (13.5) · (-0.259) = -3.49