Determine whether two vectors are orthogonal from their components Trigonometry

Two vectors are orthogonal if and only if their dot product is zero.

Here, we have:

\overrightarrow{u} \cdot \overrightarrow{v} = \dbinom{2}{3} \cdot \dbinom{-6}{4}=\left[2 \times \left(-6\right)\right]+\left(3 \times 4\right)=-12+12= 0

Two vectors are orthogonal if and only if their dot product is zero.

Here, we have:

\overrightarrow{u} \cdot \overrightarrow{v} = \dbinom{3}{5} \cdot \dbinom{-2}{4}=\left[3 \times \left(-2\right)\right]+\left(5 \times 4\right)=-6+20= 14

Two vectors are orthogonal if and only if their dot product is zero.

Here, we have:

\overrightarrow{u} \cdot \overrightarrow{v} = \dbinom{-1}{4} \cdot \dbinom{4}{1}=\left[-1 \times \left(4\right)\right]+\left(4\times 1\right)=-4+4= 0

Two vectors are orthogonal if and only if their dot product is zero.

Here, we have:

\overrightarrow{u} \cdot \overrightarrow{v} = \dbinom{-1}{3} \cdot \dbinom{3}{7}=\left[-1 \times 3\right]+\left(3 \times 7\right)=-3+21=18

Two vectors are orthogonal if and only if their dot product is zero.

Here, we have:

\overrightarrow{u} \cdot \overrightarrow{v} = \dbinom{3}{-1} \cdot \dbinom{5}{15}=\left[3 \times 5\right]+\left(-1 \times 15\right)=15-15= 0

Two vectors are orthogonal if and only if their dot product is zero.

Here, we have:

\overrightarrow{u} \cdot \overrightarrow{v} = \dbinom{2}{4} \cdot \dbinom{3}{-2}=\left[2 \times3\right]+\left(4 \times -2\right)=6-8=-2

Two vectors are orthogonal if and only if their dot product is zero.

Here, we have:

\overrightarrow{u} \cdot \overrightarrow{v} = \dbinom{2}{0} \cdot \dbinom{-5}{4}=\left[2 \times \left(-5\right)\right]+\left(0 \times 4\right)=-10+0= -10