Answer:
[tex]proj_uw=6.2i-4.2j[/tex]
Step-by-step explanation:
The projection of a vector [tex]v[/tex] onto a vector [tex]u[/tex] is defined as the projection of the vector [tex]v[/tex] on the line that contains the vector [tex]u[/tex]. It can be calculated using the following formula:
[tex]proj_uv=\frac{u\cdot v}{||u||^2} u[/tex]
Where:
[tex]u\cdot v[/tex]
Is the dot product between [tex]u[/tex] and [tex]v[/tex] which is given by:
[tex]u\cdot v= $\sum_{i=1}^{n} u_iv_i= u_1v_1+u_2v_2+...+u_nv_n$[/tex]
and:
[tex]||u||[/tex]
Is the magnitude of vector which can be calculated as follows:
[tex]||u||=\sqrt{u_1^2+u_2^2+...+u_n^2}[/tex]
In this sense, the projection of vector w onto vector u is:
[tex]proj_uw=\frac{u\cdot w}{||u||^2} u[/tex]
Where the dot product between [tex]u[/tex] and [tex]w[/tex] is:
[tex]u\cdot w =(9*19)+(-6*15)=171-90=81[/tex]
And the magnitude of [tex]u[/tex] is:
[tex]||u||=\sqrt{9^2+(-6)^2} = 3 \sqrt{13}[/tex]
Thus:
[tex]proj_uw=\frac{u\cdot w}{||u||^2} u=\frac{81}{117} \langle9,-6\rangle=\langle6.23,-4.15\rangle\approx6.2i-4.2j[/tex]
Answer:
A on edge
Step-by-step explanation:
Got it right on quiz (:
