if A=2i+j+k, B=i-2j+2k and C=3i-4j+2k , find the projection A+C in the direction of B.
A+C=(5,−3,3)B=(1,−2,2)prB(A+C)=(A+C,B)(B,B)B=5⋅1−3⋅(−2)+3⋅212+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)A+C=(5,−3,3)B=(1,−2,2)prB(A+C)=(B,B)(A+C,B)B=12+22+225⋅1−3⋅(−2)+3⋅2(1,−2,2)==(917,−934,934)
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