IB Mathematics Applications & Interpretation Question Type 7: Determining Components of Vectors That Complement Another Vector Exercises

For $\mathbf{a}=(3,2,-2)$ and $\mathbf{b}=(1,0,1)$, verify that the component of $\mathbf{a}$ perpendicular to $\mathbf{b}$ lies in the plane orthogonal to $\mathbf{b}$ by computing it.

Given $\mathbf{a}=(3,2,-2)$ and $\mathbf{b}=(1,0,1)$, find the vector component of $\mathbf{a}$ perpendicular to $\mathbf{b}$.

Given vectors $\mathbf{a}=\left(\begin{array}{c}1\\ 1\\ 1\end{array}\right)$ and $\mathbf{b}=\left(\begin{array}{c}1\\ 2\\ 2\end{array}\right)$, determine the component of $\mathbf{a}$ perpendicular to $\mathbf{b}$.

For $\mathbf{a}=(3,-1,2)$ and $\mathbf{b}=(1,4,0)$, determine the vector component of $\mathbf{a}$ parallel to $\mathbf{b}$.

Find the scalar component of vector $\mathbf{a}=\left(\begin{array}{c}5\\ 4\\ 1\end{array}\right)$ in the direction of vector $\mathbf{b}=\left(\begin{array}{c}2\\ 1\\ 6\end{array}\right)$.

Determine the vector projection of $\mathbf{a}=\left(\begin{array}{c}4\\ 5\\ 6\end{array}\right)$ onto $\mathbf{b}=\left(\begin{array}{c}-1\\ 2\\ 3\end{array}\right)$.

Find the vector projection of $\mathbf{b}=\left(\begin{array}{c}5\\ 0\\ 2\end{array}\right)$ onto $\mathbf{a}=\left(\begin{array}{c}2\\ -3\\ 1\end{array}\right)$.

For vectors $\mathbf{a}=(3,-1,2)$ and $\mathbf{b}=(1,4,0)$, find the scalar component of $\mathbf{a}$ in the direction of $\mathbf{b}$.

Compute the scalar component of $\mathbf{b}=(5,0,2)$ in the direction of $\mathbf{a}=(2,-3,1)$.

Find the vector projection of $\mathbf{a}=\left(\begin{array}{c}5\\ 4\\ 1\end{array}\right)$ onto $\mathbf{b}=\left(\begin{array}{c}2\\ 1\\ 6\end{array}\right)$.

Find the scalar component of the vector $\mathbf{a}=\left(\begin{array}{c}4\\ 5\\ 6\end{array}\right)$ in the direction of the vector $\mathbf{b}=\left(\begin{array}{c}-1\\ 2\\ 3\end{array}\right)$.

Let $\mathbf{a}=\left(\begin{array}{c}7\\ 1\\ 4\end{array}\right)$ and $\mathbf{b}=\left(\begin{array}{c}2\\ 3\\ 6\end{array}\right)$. Find the vector component of $\mathbf{a}$ perpendicular to $\mathbf{b}$.