Answer to Question #318653 in Analytic Geometry for Neyoclass

Question #318653

if A=2i+j+k, B=i-2j+2k and C=3i-4j+2k , find the projection A+C in the direction of B.


1
Expert's answer
2022-03-29T08:50:38-0400

A+C=(5,3,3)B=(1,2,2)prB(A+C)=(A+C,B)(B,B)B=513(2)+3212+22+22(1,2,2)==(179,349,349)A+C=\left( 5,-3,3 \right) \\B=\left( 1,-2,2 \right) \\pr_B\left( A+C \right) =\frac{\left( A+C,B \right)}{\left( B,B \right)}B=\frac{5\cdot 1-3\cdot \left( -2 \right) +3\cdot 2}{1^2+2^2+2^2}\left( 1,-2,2 \right) =\\=\left( \frac{17}{9},-\frac{34}{9},\frac{34}{9} \right)


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