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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 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## ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 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)##