#"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