#vec"A" = hati + hatj + hatk#
#vec"B" = hati + hatj#
Magnitude of vectors are
#|vec"A"| = sqrt(1^2 + 1^2 + 1^2) = sqrt(3)#
#|vec"B"| = sqrt(1^2 + 1^2) = sqrt(2)#
Cross product of two vectors are
#vec"A" × vec"B" = (hati + hatj + hatk) × (hati + hatj)#
#color(white)(vec"A" × vec"B") = (hati × hati) + (hati × hatj) + (hatj × hati) + (hatj × hatj) + (hatk × hati) + (hatk × hatj)#
#color(white)(vec"A" × vec"B") = 0 + hatk + (-hatk) + 0 + hatj + (-hati)#
#color(white)(vec"A" × vec"B") = hatj - hati#
Magnitude of cross product is
#|vec"A" × vec"B"| = sqrt(1^2 + 1^2) = sqrt(2)#
Angle between them is
#theta = sin^-1[(|vec"A" × vec"B"|)/(|vec"A"||vec"B"|)]#
#color(white)(θ) = sin^-1[cancel(sqrt(2))/(sqrt(3) · cancel(sqrt(2)))]#
#color(white)(θ) = sin^-1(1/sqrt(3))#
#color(white)(θ) = 35.26°#
