Question

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

Answer 1

$A+C=\left( 5,-3,3 \right) \\B=\left( 1,-2,2 \right) \\pr_B\left( A+C \right) =\frac{\left( A+C,B \right)}{\left( B,B \right)}B=\frac{5\cdot 1-3\cdot \left( -2 \right) +3\cdot 2}{1^2+2^2+2^2}\left( 1,-2,2 \right) =\\=\left( \frac{17}{9},-\frac{34}{9},\frac{34}{9} \right)$