True/False: The set of vectors, $$ is orthogonal.
True False
Two vectors are orthogonal iff their dot product is zero.
True/False: The set of vectors, $$ is orthogonal.
True False
Two vectors are orthogonal if and only if their dot product is zero.

True/False: An orthogonal basis for a subspace $$ of $$ is a basis for $$ that is also an orthogonal set.
True False

If $$ is a basis for $$, then for any $$ in $$, $$ can be written as a linear combination of $$. Given the vectors $$ and $$ below, compute the coefficients in the linear combination.

$$. (Simplify fractions as much as possible.)

$$
Let $$ and $$. Find the orthogonal projection of $$ onto $$.

First, find $$, then find $$.

Then the orthogonal projection of $$ onto $$ is $$.

Let $$ be the line through $$ and $$. The orthogonal projection of $$ onto $$ (or the orthogonal projection of $$ onto $$ ) is $$

True/False: Not every orthogonal set in $$ is linearly independent.
True False

True/False: Every orthogonal set of non-zero vectors in $$ is linearly independent.
True False

What is the definition of an orthonormal set?
An orthogonal set that is linearly independent An orthogonal basis A basis consisting only of unit vectors An orthogonal basis consisting only of unit vectors An orthogonal set consisting only of unit vectors