22.01 Introduction to vectors
Write the vector represented on the following planes as a column vector:
Consider the following figure and write the column vector for each of the following:
\overrightarrow{AB}
\overrightarrow{BC}
\overrightarrow{AC}
For each of the following graphs:
Write the vector c as a column vector.
Write the vector d as a column vector.
If A = \left( - 2 , 3\right), B = \left(1, 7\right), C = \left( - 9 , 6\right) and O is the origin, express each of the following as a column vector:
\overrightarrow{OB}
\overrightarrow{AC}
\overrightarrow{AO}
\overrightarrow{CB}
Plot the vector \begin{bmatrix}5\\9\end{bmatrix} on a number plane. Use the origin as the starting point of the vector.
Let A = \left( - 6 , 2\right), B = \left(1, 4\right), C = \left( - 3 , 5\right) and O be the origin. Plot the following vectors on a number plane:
\overrightarrow{OC}
\overrightarrow{AB}
\overrightarrow{BO}
\overrightarrow{OC}
For each of the following sets of points:
Plot the vectors \overrightarrow{AB} and \overrightarrow{CD} on on a number plane.
State whether the two vectors are equivalent.
A\left(5, 4\right), B\left(5, 9\right), C\left( - 4 , - 2 \right) and D\left( - 4 , 3\right).
A\left( - 4 , 2\right), B\left( - 6 , 6\right), C\left( - 4 , - 2 \right) and D\left( - 6 , 2\right).
A\left(3, - 4 \right), B\left(3, - 6 \right), C\left(5, 3\right) and D\left(5, 5\right).
Find the magnitude of vector a:
Find the magnitude of the vector between points A and B:
Find the magnitude of vector b:
Consider the plotted path:
Calculate the displacement of the path.
Calculate the distance of the path.
Is the displacement equal to the distance? Explain your answer.
Consider the vector defined by the directed line segment from \left( - 5 , 3\right) to \left(1, - 5 \right).
Plot the vector.
Find the magnitude of the vector.
Two vectors that are parallel can have different magnitudes. Is it true or false?
Find the exact magnitudes of the following vectors
\begin{bmatrix}8\\15\end{bmatrix}
\begin{bmatrix}-8\\-15\end{bmatrix}
\begin{bmatrix}6\\0\end{bmatrix}
\begin{bmatrix}-6\\0\end{bmatrix}
Find the exact magnitude of the vector \left(4, 8\right).
Find the magnitude of the vector \left(12, - 4 , 3\right).
If a = \left( 3 x, 4 x\right) and \left|a\right| = 15, find the value of x.
A pilot flies 12 km north and then 16 km east. Find the magnitude of the vector created from her initial position to the final position.
A boat travels 12 km west and then 5 km south. Determine the distance of the boat from its initial position.
Consider the vector 12 \mathbf{i} - 16 \mathbf{j}. Find the magnitude of the vector.
Consider the vector v = 12 \mathbf{i} - 9 \mathbf{j}. Find the magnitude of the vector.
Suppose \mathbf{a} = 9 \mathbf{i} + 12 \mathbf{j} and \mathbf{b} = 6 \mathbf{i} + 8 \mathbf{j}. Find \left|\mathbf{b}\right|.
Find the magnitude of the vector 12 \mathbf{i} + 16 \mathbf{j}.
State whether each of the following is a vector quantity:
A force of 8 \text{ N} acting horizontally right.
A displacement of 4 \text{ m} along the line joining A and B.
A mass of 1 \text{ kg}
A time of 1 second.
What is the opposite of the vector representing 800 km south?
Let \mathbf{U} = \left( - 2 , - 4 \right) be a vector. Determine the direction angle \theta of the vector correct to the nearest degree, where 0 \degree \leq \theta < 360 \degree.
Let \mathbf{U} = \left( - \dfrac{\sqrt{3}}{2} , \dfrac{1}{2}\right) be a vector. Determine the direction angle \theta of vector \mathbf{U}, where \\ 0 \degree \leq \theta < 360 \degree.
Let \mathbf{U} = 5 \mathbf{i} - 3 \mathbf{j} be a vector. Determine the direction angle \theta of vector \mathbf{U} in degrees, where 0 \degree \leq \theta < 360 \degree. Round you answer to two decimal places.
Find the direction angle \theta, in degrees, of \mathbf{u} + \mathbf{v}. Round your answer to four decimal places.
Write the vector \mathbf{u} in the form \left(a, b\right), where a and b are to four decimal places.
Write the vector \mathbf{v} in the form \left(a, b\right), where a and b are to four decimal places.
Write the vector \mathbf{u} + \mathbf{v} in the form \left(a, b\right), where a and b are to four decimal places.
Find the direction angle \theta, in degrees, of the vector \mathbf{u} + \mathbf{v} = \left( - 6.2116 , 11.5911\right). Round your answer to four decimal places.
