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

Saclar projection##1/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##
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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##
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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)##