The direction of a vector is usually defined as starting on the positive x-axis (or due East) and rotating counterclockwise.

This is the same convention used for the unit circle when studying trigonometry.

 

Notes

 

Practice Problems

\(\textbf{1)}\) Find the direction and magnitude of the vector.

Show Answer

The answer is \(|\vec{v}|=5, \theta=53.1^{\circ}\)

 

\(\textbf{2)}\) Find the direction and magnitude of the vector.

Show Answer

The answer is \(|\vec{v}|=13.9, \theta=149.7^{\circ}\)

 

\(\textbf{3)}\) \(|\vec{a}|=3, 70^{\circ}\), \( |\vec{b}|=4, 110^{\circ} \)
Find \(\vec{a}+\vec{b}\) as a magnitude and direction

Show Answer

The answer is \(|\vec{a}+\vec{b}|=6.59, \theta=93^{\circ}\)

 

See Related Pages\(\)

\(\bullet\text{ Displacement Vectors}\)
\(\,\,\,\,\,\,\,\,(x_2-x_1)\vec{i}+(y_2-y_1)\vec{j}…\)

\(\bullet\text{ Magnitude, Direction, and Unit Vectors}\)
\(\,\,\,\,\,\,\,\,|\vec{u}|=\sqrt{a^2+b^2}…\)

\(\bullet\text{ Dot Product}\)
\(\,\,\,\,\,\,\,\,a \cdot b=x_1 x_2+ y_1 y_2…\)

\(\bullet\text{ Parallel and Perpendicular Vectors}\)
\(\,\,\,\,\,\,\,\,⟨8,2⟩ \text{ and } ⟨−4,−1⟩…\)

\(\bullet\text{ Scalar and Vector Projections}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{a \cdot b}{|b|^2} \, \vec{b}…\)

\(\bullet\text{ Cross Product}\)
\(\,\,\,\,\,\,\,\,\)\(…\)

\(\bullet\text{ Equation of a Plane}\)
\(\,\,\,\,\,\,\,\,Ax+By+Cz=D…\)

\(\bullet\text{ Andymath Homepage}\)