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

1 Answer
Jul 29, 2018

Answer:

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

Explanation:

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>#