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QUESTION

How do you find the scalar and vector projections of b onto a given a = i + j + k, b = i - j + k?

Saclar projection1/sqrt3 and 1/3(hati+hatj+hatk)

We have been given two vectors veca and vec b , we are to find out the scalar and vector projection of vec b  onto vec a we have veca=hati+hatj+hatk and vecb=hati-hatj+hatk ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The scalar projection of vec b  onto vec a means the magnitude of resolved component of vec b  inthe direction of vec a and is given byThe scalar projection of vec b  onto vec a =(vecb*veca)/|veca| =((hati+hatj+hatk)*(hati-hatj+hatk))/(sqrt(1^2+1^1+1^2)) =(1^2-1^2+1^2)/sqrt3=1/sqrt3

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The Vector projection of vec b  onto vec a means the resolved component of vec b  in the direction of vec a and is given byThe scalar projection of vec b  onto vec a =(vecb*veca)/|veca|^2.(hati+hatj+hatk) =((hati+hatj+hatk)*(hati-hatj+hatk))/((sqrt(1^2+1^1+1^2))^2).(hati+hatj+hatk) =(1^2-1^2+1^2)/3.(hati+hatj+hatk)=1/3(hati+hatj+hatk)