Question

已知A的绝对值是根号3,B的绝对值是根号2,A和B的夹角为30度,求A加B的绝对值,A减B的绝对值

Answer 1

|a+b|^2=a^2+2a*b+b^2

=|a|^2+2*|a|*|b|*cos30°+|b|^2

=3+2*√3*2*√3/2+4

=13

|a+b|=√13

|a-b|^2=a^2-2a*b+b^2

=|a|^2--2*|a|*|b|*cos30°+|b|^2

=3-2*√3*2*√3/2+4

=1

|a-b|=1