What is the projection of $(8 i + 12 j + 14 k)$ $(8i + 12j + 14k)$ onto $(2i + 3j – 7k)$ ?

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Answer 1 · 2018-01-29T13:18:21

The vector projection is $=-36/sqrt62<2, 3,-7>$

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

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

$veca=<2,3,-7>$

$vecb= <8, 12,14>$

The dot product is

$veca.vecb =<2,3,-7>. <8,12,14>$

$= (2)*(8)+(3) *(12)+(-7)*(14)=16+36-84=-36$

The modulus of $veca$ is

$=||veca||=||<2,3,-7>|| =sqrt((2)^2+(3)^2+(-7)^2)=sqrt(4+9+49)=sqrt62$

Therefore,

$proj_(veca)vecb=-36/sqrt62<2, 3,-7>$

What is the projection of (8i + 12j + 14k)(8i+12j+14k)(8i + 12j + 14k) onto (2i + 3j – 7k) (2i + 3j – 7k)?