Question

How do you find a) u+v, b) u-v, c) 2u-3v given `u=3j, v=2i`?

Answer 1

`a)" "u+v=sqrt(13)" , "tan alpha=3/2`
`b)" "u-v=sqrt(13)" , "tan beta=-3/2`
`c)" "2u-3v=6sqrt(2)" , "tan theta=-1`

Explanation:

`"the vector u is shown in figure below"`

`"the vector v is shown in the diagram below"`

`"a)the vector w=u+v is shown in the diagram below"`

`w=2.i+3.j`

`"magnitude of w can be calculated :"`
`w=sqrt(2^2+3^2)`
`w=sqrt(4+9)" , "w=sqrt(13)`
`"direction of the vector w is"`
`tan alpha=3/2`

`"a)the vector z=u-v is shown in the diagram below"`

`z=-2.i+3.j`
`"magnitude of z can be calculated :"`
`w=sqrt((-2)^2+3^2)`
`w=sqrt(4+9)" , "w=sqrt(13)`
`"direction of the vector w is"`
`tan beta=-3/2`

`c)"The vector 2u is shown in the figure below"`

`"The vector 3v is shown in the figure below"`

`"p=2u-3v is shown in the figure below"`

`"magnitude of p can be calculated :"`
`p=sqrt((-6)^2+6^2)`
`p=sqrt(36+36)" , "p=sqrt(72)=6sqrt(2)`
`"direction of the vector p is"`
`tan theta=-6/6`=-1