Question

已知向量a的模等于2,向量b的模等于3,a与b的夹角为60度,则丨a-b丨等于多少?丨a-2b丨＝?

Answer 1

|a|=2,|b|=3.

|a-b|=√(a-b)^2

=√(a^2-2ab+b^2).

=√(2^2-2|a||b|cos+b^2).

=√(4-2*2*3*cos60°+3^2).

=√(4-6+9).

=√7.

|a-2b|=√[a^2-2a*2b+(2b)^2].

=√(a^2-2*2ab+4b^2).

=√(a^2-2*2|a||b|cos+4b^2).

=√[4-4*2*3*(1/2)+4^9].

=√28.

=2√7.