Question Type 7: Determining components of vectors that complement another vector Exercises

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

Find the scalar component of vector $a=(5,4,1)$ in the direction of $b=(2,1,6)$.

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

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

Find the vector projection of $a=(5,4,1)$ onto $b=(2,1,6)$.

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

Find the scalar component of $a=(4,5,6)$ in the direction of $b=(-1,2,3)$.

Find the vector projection of $b=(5,0,2)$ onto $a=(2,-3,1)$.

Let $a=(7,1,4)$ and $b=(2,3,6)$. Find the vector component of $a$ perpendicular to $b$.

Given $a=(1,1,1)$ and $b=(1,2,2)$, determine the component of $a$ perpendicular to $b$.

Determine the vector projection of $a=(4,5,6)$ onto $b=(-1,2,3)$.

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