What is the projection of #(3i + 2j - 6k)# onto # (3i - j - 2k)#?

Answer 1

The answer is #=19/(7sqrt14)(3i-j-2k)#

Let #veca=〈3,-1,-2〉# and #vecb=〈3,2,-6〉# Then the vector projection of #vecb# upon #veca# is #(veca.vecb)/(∥veca∥∥vecb∥)veca# The dot product #veca.vecb=〈3,-1,-2〉.〈3,2,-6〉=9-2+12=19# The modulus #∥veca∥=sqrt(9+1+4)=sqrt14# The modulus #∥vecb∥=sqrt(9+4+36)=sqrt49=7# the projection is #=19/(7sqrt14)〈3,-1,-2〉#

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Answer 2

Charles Aeschliman

The projection of (3i + 2j - 6k) onto (3i - j - 2k) is (9/14)i + (3/7)j - (6/7)k.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.