Notes

 

Questions

\(\textbf{1)}\) Find \(|\vec{a}|\) where \(\vec{a}=3\vec{i}-4\vec{j}\)

Show Answer

The answer is \(|\vec{a}|=5 \)

Show Work

\(\,\,\,|\vec{a}|=\sqrt{3^2+(-4)^2}\)
\(\,\,\,|\vec{a}|=\sqrt{9+16}\)
\(\,\,\,|\vec{a}|=\sqrt{25}\)
\(\,\,\,|\vec{a}|=5\)

 

\(\textbf{2)}\) Find \(|\vec{b}|\) where \(\vec{b}=3\vec{i}-4\vec{j}+6\vec{k}\)

Show Answer

The answer is \(|\vec{b}|=\sqrt{61} \)

Show Work

\(\,\,\,|\vec{b}|=\sqrt{3^2+(-4)^2+6^2}\)
\(\,\,\,|\vec{b}|=\sqrt{9+16+36}\)
\(\,\,\,|\vec{b}|=\sqrt{61}\)

 

\(\textbf{3)}\) Find \(|\vec{v}|\) where \(\vec{v}=\langle -4,5 \rangle\)

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The answer is \(|\vec{v}|=\sqrt{41} \)

 

\(\textbf{4)}\) Find \(|\vec{m}|\) where \(\vec{m}=\langle 1,7,-3 \rangle\)

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The answer is \(|\vec{m}|=\sqrt{59} \)

 

 

See Related Pages\(\)

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

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

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

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

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

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

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