Geometry
Properties of a Vector
Two vectors \(\vec{a}\), \(\vec{b}\) are shown in the diagram above. Which of the following is the same vector as \(\vec{a}+ \vec{b}\)?
Given the vectors
\[\begin{align} \vec{a} &=(1, -4),\\ \vec{b} &=(2, 3),\\ \vec{p} &=-\vec{a}+3\vec{b},\\ \vec{q} &=2\vec{a}-5\vec{b}, \end{align}\]
what is \(2\vec{p}-4\vec{q}?\)
What real values of \(x\) and \(y\) satisfy the equation \[ x(1,2)-y(2,3)=(5, 3)? \]
Which of the following is the same vector as \(\vec{c}\) in the regular hexagon below?
\[\] Details and assumptions
- Let \(\vec{AB}=\vec{a},\) \(\vec{AC}=\vec{b},\) \(\vec{AF}=\vec{c}.\)
Two vectors \(\vec{a}\), \(\vec{b}\) are shown in the diagram above. Which of the following is the same vector as \(\vec{a}- \vec{b}\) ?
