Question

Question #0b785

Answer 1

The vector projection is `=13/97<7,-8,-9>`
The scalar projection is `=26/sqrt194`

Explanation:

The vector projection of `vecA` over `vecB` is

`=(vecA.vecB)/(||vecB||^2)vecB`

`vecA=<2,-6,4>`

`vecB=<7,-8,-9>`

The dot product is

`vecA.vecB=<2,-6,4>.<7,-8,-9> =(2*7+6*8-9*4)=14+48-36=26`

The modulus of `vecB` is

`=||vecB||=||<7,-8,-9>||=sqrt(7^2+8^2+9^2)=sqrt194`

The vector projection is

`=26/194<7,-8,-9>`

The scalar projection is

`=(vecA.vecB)/(||vecB||)=26/sqrt194`