Linear Algebra and Its Applications · Problem 3.2.17

Orthogonality — Gilbert Strang

Mathematics · cosines-projections-onto-lines

Problem

Project the vector

b

onto the line through

a

. Check that

e

is perpendicular to

a

: ((a))

b = \begin{bmatrix}1\\2\\2\end{bmatrix}

and

a = \begin{bmatrix}1\\1\\1\end{bmatrix}

. ((b))

b = \begin{bmatrix}1\\3\\1\end{bmatrix}

and

a = \begin{bmatrix}-1\\-3\\-1\end{bmatrix}