What is the projection of #< -3, 6, 7># onto #< 5, -3, 8>#?

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Answer 1 · 2017-02-05T10:48:44

The vector projection is #=53/98<5,-3,8>#
The scalar projection is#=53/sqrt98#

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

#=(veca.vecb)/(||veca||^2)*veca#

The dot product is

#veca.vecb=<3,6,7>.<5,-3,8>=15-18+56=53#

The modulus of #veca# is

#||veca||=||<5,-3,8>||=sqrt(25+9+64)=sqrt98#

The vector projection is

#=53/98<5,-3,8>#

The scalar projection is

#(veca.vecb)/(||veca||)=53/sqrt98#