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Find the projection of u onto v
URGENT HELP

Find the projection of u onto v URGENT HELP-example-1
User Eik
by
7.1k points

1 Answer

3 votes

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>.

User Federico Mastrini
by
6.2k points
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