Notes

Questions

\(\textbf{1)}\) Find the displacement vector between \(A (-5,8) \) and \( B (6,0)\)

Show Displacement Vector

\(\vec{AB}\) is \(< 11,-8>\) or \(11\vec{i}-8\vec{j}\)

 

\(\textbf{2)}\) Find the displacement vector between \(A (4,2) \) and \( B (1,9)\)

Show Displacement Vector

\(\vec{AB}\) is \(< -3,7>\) or \(-3\vec{i}+7\vec{j}\)

 

\(\textbf{3)}\) Find the displacement vector between \(A (0,0) \) and \( B (1,5)\)

Show Displacement Vector

\(\vec{AB}\) is \(< 1,5>\) or \(1\vec{i}+5\vec{j}\)

 

\(\textbf{4)}\) Find the displacement vector between \(C (1,3,2) \) and \( D (4,-1,-5)\)

Show Displacement Vector

\(\vec{CD}\) is \(<3,-4,-3>\) or \(3\vec{i}-4\vec{j}-3\vec{k}\)

 

\(\textbf{5)}\) Find the displacement vector between \(C (5,1,6) \) and \( D (-3,-2,-1)\)

Show Displacement Vector

\(\vec{CD}\) is \(<-8,-3,-7>\) or \(-8\vec{i}-3\vec{j}-7\vec{k}\)

 

\(\textbf{6)}\) Find the displacement vector between \(C (1,2,3) \) and \( D (4,-5,-6)\)

Show Displacement Vector

\(\vec{CD}\) is \(<3,-7,3>\) or \(3\vec{i}-7\vec{j}+3\vec{k}\)

 

\(\textbf{7)}\) Find the initial point \((P)\) of vector \(\vec{v}\) from \(P\) to \(Q\) where \(\vec{v}= <3,8> \) and \( Q= (4,1)\)

Show Initial Point

The initial point is \((1,-7)\)

 

\(\textbf{8)}\) Find the initial point \((P)\) of vector \(\vec{v}\) from \(P\) to \(Q\) where \(\vec{v}= <-5,2> \) and \( Q= (3,-1)\)

Show Initial Point

The initial point is \((8,1)\)

 

\(\textbf{9)}\) Find the initial point \((P)\) of vector \(\vec{v}\) from \(P\) to \(Q\) where \(\vec{v}= <-4,0> \) and \( Q= (9,9)\)

Show Initial Point

The initial point is \((13,9)\)

 

See Related Pages\(\)

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

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

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

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

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

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

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