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Notes
Parallel Vectors
\(\langle x_1,y_1 \rangle \text{ and } \langle x_2,y_2 \rangle \text{ are parallel if}\)
\(\langle x_2,y_2 \rangle = \langle kx_1,ky_1 \rangle\)
Perpendicular Vectors
\(\langle x_1,y_1 \rangle \text{ and } \langle x_2,y_2 \rangle \text{ are perpendicular if}\)
\(x_1 x_2+ y_1 y_2 =0\)
Practice Questions
Are the following pairs of vectors parallel, perpendicular or neither?
\(\textbf{1)}\) \(\langle8,2 \rangle \text{ and } \langle-4,-1 \rangle\)
\(\textbf{2)}\) \(\langle3,6 \rangle \text{ and } \langle1,-2 \rangle\)
\(\textbf{3)}\) \(\langle4,-8 \rangle \text{ and } \langle4,2 \rangle\)
\(\textbf{4)}\) \(\langle1,2 \rangle \text{ and } \langle3,4 \rangle\)
\(\textbf{5)}\) \(\langle-2,4 \rangle \text{ and } \langle4,-8 \rangle\)
\(\textbf{6)}\) \(\langle3,1 \rangle \text{ and } \langle9,3 \rangle\)
\(\textbf{7)}\) \(\langle6,-2 \rangle \text{ and } \langle1,3 \rangle\)
See Related Pages\(\)
\(\bullet\text{ Displacement Vectors}\)
\(\,\,\,\,\,\,\,\,(x_2-x_1)\vec{i}+(y_2-y_1)\vec{j}…\)
\(\bullet\text{ Magnitude, Direction, and Unit Vectors}\)
\(\,\,\,\,\,\,\,\,|\vec{u}|=\sqrt{a^2+b^2}…\)
\(\bullet\text{ Dot Product}\)
\(\,\,\,\,\,\,\,\,a \cdot b=x_1 x_2+ y_1 y_2…\)
\(\bullet\text{ Parallel and Perpendicular Vectors}\)
\(\,\,\,\,\,\,\,\,⟨8,2⟩ \text{ and } ⟨−4,−1⟩…\)
\(\bullet\text{ Scalar and Vector Projections}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{a \cdot b}{|b|^2} \, \vec{b}…\)
\(\bullet\text{ Cross Product}\)
\(\,\,\,\,\,\,\,\,\)
\(…\)
\(\bullet\text{ Equation of a Plane}\)
\(\,\,\,\,\,\,\,\,Ax+By+Cz=D…\)
\(\bullet\text{ Andymath Homepage}\)
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