Porisma

Worked solution

Find a parameter from perpendicular vectors

If a=(1t2)\mathbf a=\begin{pmatrix}1\\t\\2\end{pmatrix} and b=(012)\mathbf b=\begin{pmatrix}0\\1\\2\end{pmatrix} are perpendicular, find tt.

CJC · Vectors Basic · Example 10

Answer

t=−4t=-4.

Compare your reasoning

Set the scalar product to zero

a⋅b=0⟹(1t2)⋅(012)=0⟹t+4=0⟹t=−4\mathbf a\cdot\mathbf b=0\quad\Longrightarrow\quad\begin{pmatrix}1\\t\\2\end{pmatrix}\cdot\begin{pmatrix}0\\1\\2\end{pmatrix}=0\quad\Longrightarrow\quad t+4=0\quad\Longrightarrow\quad t=-4

Both vectors are nonzero, so their perpendicularity is equivalent to a zero dot product.

How did this question go?