Magnitude of a Vector

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Notes

Notes for Magnitude of a Vector

Questions

\(\textbf{1)}\) Find \(|\vec{a}|\) where \(\vec{a}=3\vec{i}-4\vec{j}\)
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The answer is \(|\vec{a}|=5 \)
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\(\,\,\,|\vec{a}|=\sqrt{3^2+(-4)^2}\)

\(\,\,\,|\vec{a}|=\sqrt{9+16}\)

\(\,\,\,|\vec{a}|=\sqrt{25}\)

\(\,\,\,|\vec{a}|=5\)

\(\textbf{2)}\) Find \(|\vec{b}|\) where \(\vec{b}=3\vec{i}-4\vec{j}+6\vec{k}\)
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The answer is \(|\vec{b}|=\sqrt{61} \)
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\(\,\,\,|\vec{b}|=\sqrt{3^2+(-4)^2+6^2}\)

\(\,\,\,|\vec{b}|=\sqrt{9+16+36}\)

\(\,\,\,|\vec{b}|=\sqrt{61}\)

\(\textbf{3)}\) 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\(\)

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

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

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

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

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

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

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

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