Question

Find the projection of u onto v
URGENT HELP

Answer 1

Given:

Two vectors are:

`u=\left <0,6\right>`

`v=\left <2,17\right>`

To find:

The projection of u onto v.

Solution:

Magnitude of a vector
`v=\left <a,b\right>` is:

`|v|=√(a^2+b^2)`

Dot product of two vector
`v_1=\left <a_1,b_1\right>` and
`v_2=\left <a_2,b_2\right>` is:

`v_1\cdot v_2=a_1a_2+b_1b_2`

Formula for projection of u onto v is:

`Proj_vu=(u\cdot v)/(|v|^2)v`

`Proj_vu=(\left <0,6\right>\cdot \left <2,17\right>)/((√(2^2+17^2)^2))\left <2,17\right>`

`Proj_vu=(0\cdot 2+6\cdot 17)/(4+289)\left <2,17\right>`

`Proj_vu=(0+102)/(293)\left <2,17\right>`

On further simplification, we get

`Proj_vu=(102)/(293)\left <2,17\right>`

`Proj_vu=\left <(102)/(293)\cdot 2,(102)/(293)\cdot 17\right>`

`Proj_vu=\left <(204)/(293),(1734)/(293)\right>`

Therefore, the projection of u onto v is
`Proj_vu=\left <(204)/(293),(1734)/(293)\right>`.