Given v lJ and w I J find the dot product v w find the ang

Given v = -l-J and w= - I -J find the dot product v* w, find the angle between v and w; state whether the vectors are parallel, orthogonal, or neither. What is the angle between v and w? (Do not round until the final answer Then round to the nearest tenth as needed.) (c) Are vectors v and w parallel, orthogonal, or neither? neither orthogonal parallel Click to select your answers).

Solution

given v =-i -j , w =-i -j

a)v.w =(-i -j)*(-i -j)

v.w=(-1*-1)+(-1*-1)

v.w=1+1

v.w=2

b)|v|=[(-1)²+(-1)²]=2

|w|=[(-1)²+(-1)²]=2

cos(v,w) =v.w/(|v||w|)

cos(v,w) =2/(2*2)

cos(v,w) =1

(v,w)=0^o

angle beween v and w =0^o

c)v and w are parallel