What is the projection of $(8 i + 12 j + 14 k)$ $(8i + 12j + 14k)$ 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

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

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