Tag: projection

Determine the projection of A = (4,3,2,1) along B = (1,1,1,1)

by RoRi

Let $A = (4,3,2,1)$ and $B = (1,1,1,1)$ . Determine the projection of $A$ along $B$ .

From the definition, we know the projection of $A$ along $B$ is the vector $tB$ where

$T = \frac{A \cdot B}{B \cdot B} = \frac{(4,3,2,1) \cdot (1,1,1,1)}{(1,1,1,1)\cdot(1,1,1,1)} = \frac{10}{4} = \frac{5}{2}.$

Therefore, the projection of $A$ along $B$ is

$tB = \frac{5}{2}B.$

by RoRi

Let $A = (1,2,3)$ and $B = (1,2,2)$ . Determine the projection of $A$ along $B$ .

From the definition of projection of $A$ along $B$ we know the projection of $A$ along $B$ is the vector $tB$ where

$t = \frac{A \cdot B}{B \cdot B} = \frac{(1,2,3) \cdot (1,2,2)}{(1,2,2) \cdot (1,2,2)} = \frac{11}{9}.$

Therefore, the projection of $A$ along $B$ is

$tB = \frac{11}{9}B.$