Find the projection of u onto v URGENT HELP

Question

asked Jan 7, 2022 152k views

1 Answer

Federico Mastrini · Answer 1 · 2022-01-11T04:23:54+0000

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