The components of the vector in rectangular form given magnitude and angle can be found by using the following formulas: [tex]x = \|\vec r\|\cdot \cos \theta[/tex], [tex]y = \|\vec r\| \cdot \sin \theta[/tex].
Let be a vector in rectangular form, that is, a vector of the form (x, y). The magnitude can be found by applying the square root of the dot product of the vector or the Pythagorean theorem and the direction is determined by applying inverse trigonometric functions:
[tex]\|\vec r\| = \sqrt{(x,y)\,\bullet\,(x,y)}[/tex] (1)
[tex]\|\vec r \| = \sqrt{x^{2}+y^{2}}[/tex] (2)
θ = tan⁻¹ (y/x) (3)
And the components of the vector can be found by applying the following formulas:
[tex]x = \|\vec r\|\cdot \cos \theta[/tex] (4)
[tex]y = \|\vec r\| \cdot \sin \theta[/tex] (5)
The components of the vector in rectangular form given magnitude and angle can be found by using the following formulas: [tex]x = \|\vec r\|\cdot \cos \theta[/tex], [tex]y = \|\vec r\| \cdot \sin \theta[/tex].
To learn more on vectors, we kindly invite to check this verified question: https://brainly.com/question/13322477
