Notes
Questions
\(1)\) Find \(|\vec{a}|\) where \(\vec{a}=3\vec{i}-4\vec{j}\)
The answer is \(|\vec{a}|=5 \)
\(2)\) Find the unit vector in the same direction as \(\vec{a}=3\vec{i}-4\vec{j}\).
The answer is \(\frac{3}{5}\vec{i}- \frac{4}{5}\vec{j} \)
\(3)\) Find \(|\vec{b}|\) where \(\vec{b}=3\vec{i}-4\vec{j}+6\vec{k}\)
The answer is \(|\vec{b}|=\sqrt{61} \)
\(4)\) Find the unit vector in the same direction as \(\vec{b}=3\vec{i}-4\vec{j}+6\vec{k}\).
The answer is \(\frac{3}{\sqrt{61}} \vec{i}-\frac{4}{\sqrt{61}}\vec{j}+\frac{6}{\sqrt{61}}\vec{k}\) or \(\frac{3\sqrt{61}}{61}\vec{i}-\frac{4\sqrt{61}}{61}\vec{j}+\frac{6\sqrt{61}}{61}\vec{k}\)
\(5)\) Find the direction and magnitude of the vector.
The answer is \(|\vec{v}|=5, \theta=53.1^{\circ}\)
\(6)\) Find the direction and magnitude of the vector.
The answer is \(|\vec{v}|=13.9, \theta=149.7^{\circ}\)
\(7)\) \(|\vec{a}|=3, 70^{\circ}\), \( |\vec{b}|=4, 110^{\circ} \)
Find \(\vec{a}+\vec{b}\) as a magnitude and direction
The answer is \(|\vec{a}+\vec{b}|=6.59, \theta=93^{\circ}\)
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