Let \(\vec{a} = \langle -10, 4, -5 \rangle\) and \(\vec{b} = \langle -7, 2, -8 \rangle\).
Compute the projection of \(\vec{a}\) onto \(\vec{b}\) and then find the vector component of \(\vec{a}\) orthogonal to \(\vec{b}\)
\(proj_\vec{b} \vec{a} =\)
Orthogonal component =
Question 2
1 pt 1 Details
Let \(\vec{a} = \langle 4, -1, -4 \rangle\). Find a unit vector in the direction of \(\vec{a}\). Write the exact answer without
rounding numbers.
Question 3
1 pt 1 Details
Find the equation of a plane that goes through the point \((8, 4, 7)\) and that is orthogonal to the line
given by
\( \begin{cases} x(t) = -1 - t \\ y(t) = 3 + 7t \\ z(t) = 7 - 4t \end{cases} \)
