How do you find the scalar and vector projections of b onto a given #a = <3, -6, 2>#, #b = <1, 1, 1>#?

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Answer 1 · 2016-11-14T14:35:32

The scalar projection is #=-1/7#
The vector projection is #=-1/49〈3,-6,2〉#

The scalar projection of #vecb# onto #veca# is

#=(veca.vecb)/(∥veca∥)#

#veca=〈3,-6,2〉#

#vecb=〈1,1,1〉#

#veca.vecb=〈3,-6,2〉.〈1,1,1〉=3-6+2=-1#

#∥veca∥=∥〈3,-6,2〉∥=sqrt(9+36+4)=sqrt49=7#

The scalar projection is #=-1/7#

The vector projection is #(veca.vecb)/(∥veca∥)^2veca#

#=-1/49〈3,-6,2〉#