Consider the following graph and identify which vector is the result of \mathbf{a} + \mathbf{b}:
Consider the graph of vectors \mathbf{a} and \mathbf{b}. Plot the result of \mathbf{a} + \mathbf{b}.
Consider the following graphs of \mathbf{a} and \mathbf{b}:
Plot the result of \mathbf{a} + \mathbf{b} in the first graph:
Plot the result of \mathbf{b} + \mathbf{a} in the second graph:
Are the two resulting vectors \mathbf{a} + \mathbf{b} and \mathbf{b} + \mathbf{a} equal?
The vectors \mathbf{a}, \mathbf{b} and \mathbf{c} have been graphed as shown:
Plot the result of \mathbf{a} + \mathbf{b}+ \mathbf{c} on the same axes.
Vectors \mathbf{a}, \mathbf{b}, \mathbf{c} and \mathbf{d} have been graphed as shown:
Plot the result of \mathbf{b}+ \mathbf{c} on the same axes.
Rewrite \left(6, 5\right) + \left(7, - 4 \right) as a single vector.
For each of the following set of vectors, find:
Let \mathbf{a}=\begin{bmatrix}2\\4\end{bmatrix}. Using the origin as the starting point, plot the following vectors:
3 \mathbf{a}
- 2 \mathbf{a}
\dfrac{1}{2} \mathbf{a}
Consider vectors \mathbf{a} and \mathbf{b} plotted on the graph below. Find the column vector for each of the following:
\mathbf{a} + \mathbf{b}
3 \mathbf{b}
4 \mathbf{a}
5 \mathbf{b} - \mathbf{a}
3 \mathbf{a} - 4 \mathbf{b}
Consider the vectors shown below:
Which vector is equivalent to 2 \mathbf{a}?
Which vector is equivalent to \dfrac{1}{4} \mathbf{b}?
Which vector is equivalent to - \mathbf{a}?
Which vector is equivalent to - \dfrac{1}{2} \mathbf{d}?
Consider the vectors plotted on the graph. Find the column vector for each of the following:
3 \mathbf{a}
4 \mathbf{c}
2 \mathbf{b} + \mathbf{d}
\mathbf{c} - \mathbf{d}
3 \mathbf{a} - \mathbf{b}
- 4 \mathbf{b} + 2 \mathbf{c}
If \mathbf{a} = \left( 2 x, 8 x\right), \mathbf{b} = \left( 3 x, 4 x\right), and \left|\mathbf{a} + \mathbf{b}\right| = 13, find the value of x.
If \mathbf{a} = \left( 2 x, 4\right), \mathbf{b} = \left( 3 x, 8 x\right), and \left|\mathbf{a} + \mathbf{b}\right| = 13 x, find the value of x.
Consider the vectors \mathbf{a} = - 2 \mathbf{i} + 3 \mathbf{j} and \mathbf{b} = 7 \mathbf{i} + 9 \mathbf{j}.
Find \mathbf{a} + \mathbf{b}.
Find \left|\mathbf{a} + \mathbf{b}\right|.
Consider the vectors \mathbf{a} = - \mathbf{i} + 2 \mathbf{j} and \mathbf{b} = - 5 \mathbf{i} - \mathbf{j}.
Find \mathbf{a} - \mathbf{b}.
Find \left|\mathbf{a} - \mathbf{b}\right|.
Consider the vectors \mathbf{a} = 12 \mathbf{i} - 9 \mathbf{j} and \mathbf{b} = - 8 \mathbf{i} + 6 \mathbf{j}.
Find \left|\mathbf{a}\right|.
Find \left|\mathbf{b}\right|.
Find \mathbf{a} + \mathbf{b}.
Find \left|\mathbf{a} + \mathbf{b}\right|.
Is \left|\mathbf{a}\right| + \left|\mathbf{b}\right| = \left|\mathbf{a} + \mathbf{b}\right|?
Let \mathbf{a} = 3 \mathbf{i} + 4 \mathbf{j} and \mathbf{b} = 6 \mathbf{i} + 8 \mathbf{j}.
Find \left|\mathbf{a}\right|.
Find \left|\mathbf{b}\right|.
Find 5 \left|\mathbf{b}\right|.
Find \left| 2 \mathbf{a}\right|.
Find \left| 4 \mathbf{a} - 3 \mathbf{b}\right|.