Question

已知向量a=1,向量a乘以向量b等于1/4,(a+b)乘以(a-b)等于1/2,求b模的值,求向量a-b与a+b夹角的余

Answer 1

|a|=1

a*b=1/4

(a+b)*(a-b)=|a|^2-|b|^2=1/2

|b|^2=|a|^2-1/2=1-1/2=1/2

|b|=√2/2

|a+b|^2=|a|^2+2a*b+|b|^2=1+1/2+1/2=2

|a+b|=√2

|a-b|^2=|a|^2-2a*b+|b|^2=1-1/2+1/2=1

|a-b|=1

cos=(a-b)*(a+b)/(|a-b|*|a+b|)=(1/2)/√2=√2/4