What is the projection of #<4,0,1 ># onto #<6,-3,7 >#?

1 Answer
Narad T.
Dec 23, 2016

The answer is #=31/94〈6,-3,7〉#

Explanation:

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

#=(veca.vecb)/(∥veca∥)^2veca#

The dot product is #=veca.vecb#
#=〈4,0,1〉.〈6,-3,7〉=(24+0+7)=31#

The modulus of #veca# is #=∥veca∥=∥〈6,-3,7〉∥#

#=sqrt(36+9+49)= sqrt94#

The vector projection is #=31/94〈6,-3,7〉#

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