Question

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 \( \begin{cases} x(t) = -1 - t \\ y(t) = 3 + 7t \\ z(t) = 7 - 4t \end{cases} \)

          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
\( \begin{cases} x(t) = -1 - t \\ y(t) = 3 + 7t \\ z(t) = 7 - 4t \end{cases} \)

Let a⃗ = ⟨ -10, 4, -5 ⟩ and b⃗ = ⟨ -7, 2, -8 ⟩.
Compute the projection of a⃗ onto b⃗ and then find the vector component of a⃗ orthogonal to b⃗
projb⃗a⃗ =
Orthogonal component =
Question 2
1 pt 1 Details
Let a⃗ = ⟨ 4, -1, -4 ⟩. Find a unit vector in the direction of a⃗. 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
x(t) = -1 - t
y(t) = 3 + 7t
z(t) = 7 - 4t

Added by Erin H.

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