If `hat(i) and hat(j)` are unit vectors x and y axes repsectively , what is the magnitude and direction of `hat(i) + hat(j) and hat(i) - hat(j)` ?

Answer

`sqrt(2)` units `45^(@)` (b) `sqrt(2)` units , `-45^(@)`

Explanation

`(hat(i)+hat(j))=sqrt(1^(2)+1^(2)-2xx1xx cos90)-sqrt(2)2 , tan theta - | hat(j)| .|hat(i)|=I `
So `theta = 45^(@) |hat(i)-hat(j)|=sqrt(2) , tan theta = - 1, theta = - 45^(@)`