What is the projection of #(8i + 12j + 14k)# onto # (3i – 4j + 4k)#?

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Answer 1 · 2018-07-29T13:18:15

The projection is #=(32)/41*<3,-4,4>#

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

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

Here,

#veca= <3,-4,4>#

#vecb = <8,12,14>#

Therefore,

The dot product is

#veca.vecb=<3,-4,4> . <8,12,14> =24-48+56=32#

The modulus of #veca# is

#|veca| = |<3,-4,4>| = sqrt(9+16+16)= sqrt41#

Therefore

#proj_(veca)vecb=(32)/41*<3,-4,4>#