Addition of vectors
Vectors are added 鈥榥ose to tail鈥 as shown below.
The addition of the vectors is the line from the starting point to the finishing point.
Question
Write as single vectors:
- f + g
- a + b
- e - b - a
- e
- -c (Did you remember the minus sign?)
- -d
Question
Triangles ABC and XYZ are equilateral.
X is the midpoint of AB, Y is the midpoint of BC, Z is the midpoint of AC.
\(\overrightarrow {AX} = a,\,\overrightarrow {XZ} = b\,,\,\overrightarrow {AZ} = c\)
Express each of the following in terms of a,b and c.
- \(\overrightarrow {XY}\)
- \(\overrightarrow {YZ}\)
- \(\overrightarrow {XC}\)
- \(\overrightarrow {BZ}\)
- \(\overrightarrow {AC}\)
Remember:
Two vectors are equal if they have the same magnitude and direction, regardless of where they are on the page.
- c
- -a Remember that \(\overrightarrow {YZ}\) is parallel to \(\overrightarrow {AX}\) and of the same length, but the direction is different.
- b + c (It is also possible to move from X to A, and then on to C. This would give the answer -a + 2c. How many other answers can you think of?)
- b - a or 2b - c or -2a + c
- 2c
More guides on this topic
- Determine the gradient of a straight line
- Circle geometry
- Calculating the volume of a standard solid
- Applying Pythagoras Theorem
- Applying the properties of shapes to determine an angle
- Using similarity
- Working with three-dimensional coordinates
- Using vector components
- Calculating the magnitude of a vector
- An Approximate History of Co-ordinates