Answer:
(a) At U = 3, 9 , v = 4, 2, the projection of u onto v is w1=<2,8>
(b)At U = 3, 9 , v = 4, 2, the vector component of u orthogonal to v is w2 = <4,-1>
Explanation:
A
The projection of u onto v is given by:
w1= projvu = (u⋅v||v||2)v
Given that u= <6,7> and v=<1,4>, we can find the projection of u onto v as shown below:
w1= projvu = (u⋅v||v||2v=(<6,7>⋅<1,4><1,4>⋅<1,)
=(6⋅1+7⋅41⋅1+4⋅4)<1,4>
=3417<1,4>
=<2,8>
Part B
The vector component of u orthogonal to v is given by:
Using the given vectors and the projection found in part (a), we can find the vector component of u orthogonal to v as shown below:
w2=u−projvu
=<6,7≻<2,8>
=<(6−2),(7−8)>
=<4,−1>
To learn more about vector component, click brainly.com/question/17016695
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