contestada

A vector is given by R 2i + j+3k. Find (a) magnitudes of the x, y, and z components; (b) the ma nitude of R; and (c) the angles between R and the x, y, and z axes.

Respuesta :

Answer:

given,

R = 2i + j+3k

a) magnitude in x = 2

                          y = 1

                          z = 3

b) magnitude of R

[tex]R = \sqrt{2^2+1^2+3^2}[/tex]

R = 3.74 units

c) angle between the R and  the x, y, and z axes.

[tex]cos \theta_x=\dfrac{2}{3.74}[/tex]

θ x = 57.72°

[tex]cos \theta_y=\dfrac{1}{3.74}[/tex]

θ y = 74.51°

[tex]cos \theta_z=\dfrac{3}{3.74}[/tex]

θ z = 36.68°

facundo3141592

For the given vector we have:

a) The magnitudes of the components are:

  • x = 2
  • y = 1
  • z = 3

b) |R| = √14

c) x-axis: 26.56°

   y-axis:  63.4°

   z-axis:  33.7°

How to work with vectors?

Remember that:

  • versor i projects on the x-axis.
  • versor j projects on the y-axis.
  • versor k projects on the z-axis.

So we can write:

R = (2, 1, 3)

a)

The magnitudes of the components are:

  • x = 2
  • y = 1
  • z = 3

b) The magnitude of R is:

|R| = √( 2^2 + 1^2 + 3^2) = √14

c) The angle between R and x-axis is given by:

Atan(y-component/x-component) = Atan(1/2) = 26.56°

Between the R and y-axis is:

Atan(x-component/y-component) =  Atan(2/1) = 63.4°

Between R and the z-axis is:

Atan(x-component/z-component) = Atan(2/3) = 33.7°

If you want to learn more about vectors, you can read:

https://brainly.com/question/3184914